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LONGMANS,    GREEN     AND     CO. 

LONDON,  NEW  YORKt  BOMBAY,  CALCUTTA,  AND  MADRAS. 


COMPLEX    IONS 

IN   AQUEOUS  SOLUTIONS 


COMPLEX     IONS 

IN    AQUEOUS    SOLUTIONS 


♦    BY 

ARTHUR   JAQUES,    D.Sc,    F.I.C. 


LONGMANS,     GREEN     AND     CO, 

39     PATERNOSTER     ROW,     LONDON 
FOURTH  AVENUE  &  80th  STREET,  NEW  YORK 

BOMBAY,    CALCUTTA,    AND    MADRAS 
1914 


LIBRARY 

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PREFACE 

In  compiling  this  volume  the  needs — and  criticism — of  a 
large  class  of  students  unversed  in  physical  chemistry  have 
been  especially  kept  in  view,  and  it  is  considered  that  the 
introduction  of  some  elementary  matter,  such  as  proofs  of 
formula?,  which  the  advanced  reader  will  not  require,  is  by 
no  means  out  of  place. 

In  giving  an  account  of  the  methods  in  Chapters  III.-VL, 
it  was  found  necessary  to  introduce  examples,  but  these  were 
made  as  brief  as  possible  in  order  to  avoid  confusing  these 
chapters  with  the  later  ones  which  deal  with  practical 
investigations,  where  more  than  one  method  is  generally 
used  at  a  time.  The  tension  experiments  in  Chapter  VIII. 
form  a  method  of  investigation  in  which  the  examination  of 
different  salts  shows  so  little  variation  that  it  appeared 
unnecessary  to  devote  a  separate  chapter  to  the  method. 

The  chief  aim  of  the  book  is  to  give  some  account  of  the 
more  important  experimental  work  in  this  subject,  and  no 
apology  is  offered  for  the  absence  of  theories  of  valency. 

Chapter  X.  contains  an  account  of  some  results  besides 
the  identification  of  complex  compounds,  which  have  been 
arrived  at  by  similar  methods,  and  which  are  likely  to  form" 
the  basis  of  further  experiments. 

A.  J. 

POLMONT, 

Stirlingshire, 
May,  1914. 


CONTENTS 


CHAPTKR  PAGK 

I.    Introduction 1 

II.     The  Chemical  Method G 

III.  The  Ionic  Migration  Method 11 

IV.  The  Distribution  Method 20 

V.    The  Solubility  Method 28 

VI.     The  Electrical  Potential  Method 39 

VII.     Some  Examples 49 

VI II.     Ammoniac al  Salt  Solutions,  Etc. 73 

IX.     Some  Cobalt  and  Copper  Solutions 97 

X.     Some  Special  Cases  of  Equilibrium 104 

Appendix  I.     The  Hydrate  Theory 139 

H.     A   Theoretical    Method     of    examining 

Certain  Solutions 145 

Name  Index 147 

Subject  Index 150 


vi 


CHAPTER    I 

INTRODUCTION 

A.  Introductory. 

The  suggestion  that  the  abnormal  behaviour  of  certain 
electrolytes  might  be  accounted  for  by  assuming  the  for- 
mation of  complex  ions  in  them  was  first  put  forward  by 
Hittorf,  who,  in  the  course  of  his  study  of  migration,  made 
the  classical  discovery  that  the  migration  ratio  for  the  anion 
in  solutions  of  many  double  salts  and  certain  single  ones 
increased  rapidly  with  increase  in  the  concentration  of  the 
solution  and  at  high  concentrations  became  greater  than 
unity.  Hittorf  suggested  that  this  was  due  to  the  formation 
of  a  "double  salt"  in  the  solution,  which  gradually  dis- 
sociated on  dilution.  In  this  way  our  knowledge  of  the 
mode  of  ionisation  of  a  number  of  salts  in  solution  was 
established. 

Later,  the  subject  was  investigated  by  other  methods, 
notably  by  pure  chemical  means  and  by  cryoscopic  measure- 
ments. The  latter  method,  however,  yields  somewhat 
uncertain  results. 

A  new  method  was  introduced  by  Eoloff  (Zeit.  phys. 
Chem.,  13,  341  (1894)),  who  measured  the  distribution  ratio 
of  a  solute  between  two  solvents,  and  showed  that  the  in- 
crease in  the  solubility  of  bromine  in  water  observed  on 
adding  potassium  bromide  to  the  system  is  due  to  the  for- 
mation of  the  complex  ion  Br3'.  Two  years  later  Jakowkin 
(Zeit.  phys.  Chem.,  20,  19  (1896)),  employing  the  same 
method,  found  that  solutions  of  iodine  and  potassium  iodide 
show  similar  behaviour. 

In  the  last  fifteen  years  two  new  methods  of  investigating 

l  B 


2  COMPLEX   IONS 

the  constitution  of  electrolytes  have  been  worked  out,  the 
first  based  upon  solubility  measurements  and  the  second 
upon  measurements  of  electrode  potential,  and  a  large 
number  of  complex  ions  have  been  discovered  and  studied  by 
these  methods.  Much  of  this  work  was  carried  out  by  the 
late  Professors  Abegg  and  Bodlander  and  their  pupils. 

Such  investigations  are  likely  to  be  of  value  in  framing  a 
theory  of  chemical  combination  in  the  future.  For  in  com- 
plex ions  we  have  a  class  of  compounds  in  which  valencies 
other  than  the  normal  valencies  of  the  elements  entering 
into  them  are  exercised,  and  whose  dissociation  constants 
can  in  some  cases  be  measured,  so  that  we  can  gain  some 
information  about  the  action  of  these  weaker  valencies. 

An  ingenious  theory  of  valency  which  is  specially  applic- 
able to  the  formation  of  so-called  molecular  compounds 
(including  complex  ions)  has  been  constructed  by  Abegg  and 
Bodlander  (Abegg  and  Bodlander,  Zeit.  anorg.  Chem.,  20,  471 
(1899);  Abegg,  Zeit.  anorg.  Chem.,  39,  333  (1904)).  Accord- 
ing to  this  theory,  the  tendency  which  an  element  exhibits 
to  form  complex  compounds  depends  largely  upon  its 
electroaffinity,  i.e.  the  free  energy  with  which  it  takes  up  an 
electric  charge  and  becomes  converted  into  an  ion.  It  is 
assumed  that  the  electrolytic  potential  is  an  approximate 
measure  of  this  quantity,  though,  as  Abegg  and  Bodlander 
point  out,  this  would  only  be  true  if  the  concentration  of 
free  atoms  in  saturated  solution  were  the  same  for  all 
elements.  Actually,  nothing  at  all  is  known  of  the  relative 
solubilities  of  the  metals  in  water,  and  in  the  case  of  oxygen 
and  the  halogens  it  is  very  unlikely  that  at  a  given  pressure 
the  concentrations  of  the  free  atoms  in  aqueous  solutions  are 
equal.  It  is,  however,  true  that,  generally  speaking,  the  less 
the  electrolytic  potential  (either  positive  or  negative)  of  an 
element,  the  greater  is  its  tendency  to  enter  into  complex 
compounds.  The  electrolytic  potential  also  shows  a  certain 
relationship  to  the  atomic  volume,  the  two  quantities  being 
roughly  parallel  in  any  given  group  in  the  periodic  system. 
In  the  horizontal  rows,  the  electroaffinity  shows  a  continuous 


INTRODUCTION  3 

diminution  as  we  pass  from  left  to  right,  except  in  the  cases 
of  the  first  two  subsidiary  groups,  namely,  of  the  three  pairs 
of  elements,  copper  and  zinc,  silver  and  cadmium,  gold  and 
mercury.  In  these  cases  the  electroaffinity  rises  rapidly  as 
we  pass  from  left  to  right. 

Abegg  distinguishes  two  kinds  of  valency,  which  he  calls 
"  normal "  and  "  contra  "-valency  respectively.  The  normal 
valencies  of  an  element  are  those  which  are  usually  active, 
while  the  contra-valencies  are  those  which  are  only  occasion- 
ally called  into  play,  as  in  molecular  compounds,  and  are 
always  of  opposite  sign  to  the  normal  ones.  From  a  con- 
sideration of  valency  in  relation  to  the  periodic  table,  he 
suggests  that  the  total  number  of  valencies  of  all  elements 
is  eight.  Usually  less  than  this  number  are  called  into 
action. 

B.  Definition  of  the  term  "  Complex  Ion." 
A  definition  of   the  term  "complex  compound"  which 
enables  us  to  study  the  subject  according  to  a  definite  system 
was  given  by  Abegg  and  Bodlander  (loc.  tit.).     According  to 
this  definition 

Complex  compounds  are  those  in  which  a  part  of  the 
compound  which  forms  an  ion  by  electrolytic  dissociation 
consists  of  a  molecular  compound  of  a  molecule  capable 
of  forming  a  separate  ion  with  an  electrically  neutral 
molecule. 

By  the  term  "  Complex  Ion  "  we  understand  this 

molecular  compound  when  it  has  taken  up  its  natural 

electric  charge. 

A  complex  ion  consists  of  one  or  more  "  separate  ions  " 

and  a  neutral  part.     This  neutral  part  may,  in  terms  of  the 

theory,  contain  one  or  more  neutral  molecules,  but  in  all  the 

complex  compounds  that  have  been  studied  as  yet  only  one 

neutral  molecule  has  been  found. 

For  example,  potassium  ferrocyanide  consists  of  the  two 
ion-forming  parts  4K  and  Fe(CN)6.  The  latter  part  may  be 
regarded  as  a  molecular  compound  of  the  separate  ion-form- 
ing parts  4CN  and  the  neutral  molecule  Fe(CN)2.      It  forms 


4  COMPLEX   IONS 

the  complex  ion  Fe(CN)6"",  which  is  a  molecular  compound 
of  the  separate  ions  CN'CN'CN'CN'  and  the  neutral  part 
Fe(CN)2. 

It  may  be  asked  whether  this  definition  includes  all  ions 
which  can  be  regarded  as  formed  from  a  known  neutral 
molecule  and  another  ion ;  for  example,  is  S04"  a  complex 
ion  which  could  conceivably  be  formed  from  S03  and  an 
oxygen  ion  ? 

Abegg  (loc.  tit.)  says  Yes ;  oxy-acids  are  to  be  regarded 
as  complex  compounds  yielding  complex  anions,  which  con- 
sist of  a  neutral  part  (the  anhydride  of  the  acid)  and  one  or 
more  oxygen  ions.  The  oxygen  ions  are  attached  to  the  mole- 
cule of  acid-forming  oxide  by  the  positive  contra- valencies 
of  the  oxygen  atom  and  the  negative  normal  valencies 
of  the  element  forming  the  oxide.  Thus,  such  ions  may 
be  represented  by  the  formula?  S03.0",Cl207.0",N205.0",  etc. 
A  similar  argument  applies  to  the  thio-acids,  such  as  H3AsS3, 
etc.  This  suggestion  is  ingenious,  but  somewhat  speculative. 
We  shall,  therefore,  confine  ourselves  to  the  consideration  of 
complex  ions  in  which  valencies  other  than  the  ordinarily- 
accepted  valencies  of  the  elements  concerned  are  certainly 
called  into  action. 

Definition  of  the  term  " Molecular  Compound" 
In  the  definition  given  above  of  complex  compounds  and 
complex  ions  we  have  used  the  term  "  molecular  compound," 
and  for   the  sake  of  completeness  we  may  define  this  as 
follows : — 

Molecular    Compounds   are  compounds  of  two  or 

more  molecules  with  one  another,  or  of  one  or  more 

molecules  with  one  or  more  atoms  or  ions,  in  which  the 

molecules,  atoms,  or  ions  are  held  in  combination  with 

one  another  by  valencies  which  were  not  in  action  in  the 

single  components  before  combination. 

From  this  definition  it  follows  that  all  double  salts  are 

to  be  classed  as  molecular  compounds.     Most  of  these  yield 

complex  ions  in  solution,  but  in  very  varying  quantities, 

i.e.  the  complex   ions  are  of  various  degrees  of  stability. 


INTRODUCTION  5 

Thus,  we  can  have  an  indefinitely  long  series  of  salts  lying 
between  the  stages  where  complex-formation  and  dissocia- 
tion respectively  are  complete.  Extreme  examples  are  potas- 
sium ferrocyanide  on  the  one  hand,  where  the  dissociation 
of  the  Fe(CN)6""  ion  is  so  small  that  no  ferro-ion  is  recog- 
nisable in  its  solutions  by  chemical  means ;  and,  on  the  other 
hand,  the  alums,  in  dilute  solutions  of  which  at  most  only 
minimal  quantities  of  complex  ions  exist  (see  Abegg  and 
Bodlander,  loc.  cit.).  The  tests  for  small  amounts  of  com- 
plex ions  are,  however,  by  no  means  delicate,  and  even  in  the 
case  of  double  salts  where  no  complex-formation  is  recog- 
nizable, it  seems  highly  probable  that  the  difference  from 
salts  forming  more  stable  complexes  lies  only  in  the 
intensities  of  the  affinities  concerned. 

On  the  other  hand,  some  complex  ions  are  formed  in 
solution  which  do  not  correspond  to  any  known  solid  salt. 


CHAPTEK  II 

THE  CHEMICAL  METHOD 

Practically  all  metallic  salts  become  ionised  on  solution  in 
water,  and  all  reactions  between  them  are  reactions  between 
ions.  With  the  exception  of  cases  where  a  stable  complex 
is  formed  or  a  very  insoluble  compound  precipitated  the  ions 
present  in  recognisable  quantities  in  a  solution  obtained  by 
mixing  two  electrolytes  are  those  contributed  by  the  two 
single  electrolytes,  subject  to  comparatively  small  alterations 
in  concentration  due  to  differences  in  the  strengths  of  the 
original  solutions  and  reactions  tending  to  produce  more  or 
less  of  the  undissociated  salts.  (The  last  case  may  be  held 
to  include  the  precipitation  of  a  salt  which  is  not  very  in- 
soluble, with  respect  to  which  the  solution  may  become 
supersaturated.)  Thus,  if  we  mix  solutions  of  silver  nitrate 
and  potassium  sulphate  all  the  four  ions  will  be  recognisable 
in  the  resulting  solution.  If  the  original  solutions  were 
strong  some  silver  sulphate  may  be  precipitated,  but  on 
filtering  this  off  the  solution  will  be  found  to  contain  the 
ions  Ag-,  N<V,  K-,  and  S04". 

Suppose  that  instead  of  using  potassium  sulphate  we  add 
potassium  cyanide  to  a  solution  of  silver  nitrate  in  small 
quantities  at  a  time.  At  first  silver  cyanide  is  precipitated. 
If  we  stop  adding  the  potassium  cyanide  when  precipitation 
is  just  complete  we  can  show  by  analysis  that  all  the  silver 
has  been  removed  from  the  solution,  and  that  it  is  all 
precipitated  as  cyanide.  If  now  we  continue  to  add 
potassium  cyanide  to  the  solution  containing  the  precipitate 
the  silver  cyanide  begins  to  redissolve,  and  when  we  have 
added  just  as  much  more  potassium  cyanide  as  was  originally 

6 


THE  CHEMICAL   METHOD  7 

required  for  the  precipitation,  shaking  the  mixture  all  the 
time,  we  find  that  all  the  silver  cyanide  has  again  gone  into 
the  solution.  Clearly  the  solution  now  contains  silver,  and 
at  the  same  time  does  not  contain  a  recognisable  amount  of 
silver  ions,  since  ordinary  analytical  tests  fail  to  indicate 
their  presence.  The  only  means  by  which  the  silver  can 
be  precipitated  consists  in  the  addition  of  a  sulphide  solu- 
tion, and  even  in  this  case  the  precipitation  is  not  quite 
complete.  If  the  liquid  be  allowed  to  evaporate,  the  salt 
KAg(CN)2  is  obtained. 

The  reaction  during  precipitation  is 

KCN  +  Ag]Sr03  =  KN03  +  AgCN 

or,  in  terms  of  the  reacting  ions, 

ON'  +  Ag-  =  AgCN 

the  K*  and  N03'  ions  remaining  unchanged.  From  our 
study  of  the  process  of  solution  of  the  silver  cyanide  by 
addition  of  more  potassium  cyanide,  we  know  further  that 
one  molecule  of  KCN  causes  one  molecule  of  AgCN  to 
dissolve,  forming  a  compound  yielding  (analytically)  no  silver 
ions.  Two  potassium  ions  are  still  present,  corresponding 
to  the  two  stages  of  the  reaction,  and  therefore  it  must  be  the 
cyanogen  ion  that  has  reacted  with  the  silver  cyanide  to 
form  this  new  compound. 

Now,  in  all  solutions  containing  ions  the  algebraic  sum 
of  the  electric  charges  must  be  zero ;  and  to  balance  the 
potassium  ion  introduced  in  the  process  of  dissolving  the 
silver  cyanide,  the  compound  which  has  been  formed  by 
the  union  of  a  cyanogen  ion  with  a  molecule  of  silver  cyanide 
must  have  one  negative  charge.  We  might,  therefore,  con- 
clude with  a  strong  probability  of  being  right  that  the 
compound  formed  was  the  complex  ion  Ag(CN)2',  or,  allowing 
for  the  possibility  of  two  or  more  molecules  associating, 
Agm(CN)2m,  with  m  negative  charges. 

The  method  is  simpler  and  perhaps  more  certain  in  the 
case  of  very  stable  complex  ions.  Here  we  find  the  com- 
plex ion  persisting  throughout  a  series  of  stable  salts,  such 


8  COMPLEX  IONS 

as  the  ferro-  and  ferri-cyanides.  The  method  of  replacement 
has  been  successfully  employed  by  Werner  and  his  pupils 
in  investigating  a  very  large  number  of  salts  having  complex 
kations  containing  respectively  cobalt,  chromium,  platinum, 
iridium,  nickel,  iron,  manganese,  and  other  metals. 

For  example,  cobaltic  chloride  forms  with  ammonia 
luteocobalt  chloride,  Co(NH3)6Cl3.  All  three  of  the  chlorine 
atoms  are  precipitated  immediately  by  silver  nitrate  in 
the  cold,  leaving  a  solution  containing  luteocobalt  nitrate, 
Co(NH3)6(N03)3.  The  complex  ion  CO(NH3)6-  forms  a  series 
of  well-defined  salts  from  which  a  solution  of  the  free  base 
Co(NH3)6(OH)3  can  be  obtained.  Further,  the  luteocobalt 
salts  react  with  potassium  platino-  and  platinichlorides 
yielding  potassium  chloride  and  the  corresponding  salts  of 
the  complex  base.  In  these  salts  both  anion  and  kation  are 
complex.  Thus  with  potassium  platinicyanide  the  following 
reaction  occurs : — 

2Co(NH3)6Cl3  +  3K2PtCl6  =  6KC1  +  (Co(NH3)6)2(PtCl6)3 

We  thus  have  the  strongest  evidence  on  chemical  grounds 
for  the  existence  of  the  complex  kation  Co(NH3)6"\ 

When  a  salt  formed  from  this  complex  ion  loses  one 
molecule  of  ammonia  another  series  of  salts  is  obtained, 
namely,  the  purpureo  salts  having  the  general  formula 
(Co(NH3)5E)X2,  in  which  E  and  X  may  be  the  same  or 
different  negative  groups.  In  these  only  two  of  the  acid 
residues  form  ions,  so  that  if  we  allow  the  salt  (Co(NH3)5Cl)Cl2 
to  react  with  silver  nitrate,  two-thirds  of  the  chlorine  is  pre- 
cipitated while  the  remainder  stays  in  solution.  As  in  the 
case  of  the  luteo  salts,  so  also  in  this  case  the  purpureo 
salts  react  with  sodium  or  potassium  platinichloride  yielding 
salts  of  the  type  (Co(NH3)5E)PtCl6.  This  loss  of  ammonia 
accompanied  by  the  absorption  of  the  acid  residue  into  the 
complex  ion  can  be  continued,  yielding,  for  example,  the 
compound  (Co(N"H3)4Cl2) CI,  which  dissociates  into  the  mono- 
valent complex  kation  Co(KH3)4C]2*  and  the  anion  CI',  and 
next  the  compound  Co(NH)3Cl3,  which  does  not  dissociate 


THE   CHEMICAL  METHOD  9 

at  all.  The  analogous  compound  Ir(NH)3Cl3  can  be  heated 
to  boiling  with  sulphuric  acid  without  losing  HC1.  Still 
another  negative  radical  can  be  substituted  for  ammonia, 
giving  compounds  of  the  type  (M(NH3)2X4)R,  R  being  now 
a  positive  radical.  The  next  stage  is  not  known  as  yet,  but 
very  numerous  examples  of  the  final  stage  have  been  dis- 
covered, e.g.  Co(N02)6K3.  So  far  we  have  referred  only  to 
trivalent  metals.  Similar  series  of  compounds  have  been 
discovered  in  the  case  of  metals  with  valencies  other  than 
three,  such  as  platinous  and  platinic  compounds,  nickelous 
compounds,  etc. 

Werner  and  Miolati  (Zeit.  phys.  Chem.,  12,  34  (1893) ; 
14,  506  (1894))  measured  the  electrical  conductivity  of 
solutions  of  a  number  of  complex  ammonia  salts  of  platinum, 
cobalt  and  chromium,  and  showed  that  they  could  be  divided 
in  this  way  into  classes  yielding  one,  two,  three,  or  four  ions 
in  addition  to  the  complex  ion.  The  following  eight  salts 
yielding  one  free  ion  gave  values  for  the  molecular  conduc- 
tivity at  25°  ranging  from  96*7  to  108*5:  (Pt(NH3)3Cl3)Cl; 
(Pt)(NH3)3Cl)Cl  ;  (Pt(NH3)Cl5)K  ;         (Pt(NH3)Cl3K  ; 

(Co(NH3)2(]Sr02)4)K ;  (Co(C03)(NH3)4)Cl ;  and  the  two 
stereoisomeric  salts  of  the  formula  (Co(N02)2(NH3)4)Cl 
(Croceo-  and  flavo- cobalt  chlorides). 

Sixteen  salts  yielding  two  free  ions  gave  values  between 
234-4  and  267*6,  namely,  (Pt(NH3)4)Cl2;  (Pt(NH3)4Cl2)Cl2 ; 
(Pt(NH3)4(N02)2)(N03)2;  (PtCl4)K2 ;  (PtCl6)K2  ;  (Co(N02)- 
(NH3)5)(N02)2  ;  (CoBr(NH3)5)Br2  ;  (CoCl(NH3)5)Cl2  ; 
(Co(N03)(JSrH3)5)Cl2 ;  (Co(N02)(NH3)5)Cl2  (two  isomeric 
forms  examined) ;  (CrCl(NH3)5)Cl2 ;  (CrCl(NH3)4H20)Cl2  ; 
(CrCl(NH3)4H20)Br2 ;  (CrCl(NH3)4H20)(N03)2 ;  (CrN02- 
(NH3)5)C12. 

The  following  seven  salts  yielding  three  free  ions 
were  examined  and  gave  values  from  383*8  to  426"9 : 
(Co(NH3)6)Br3  ;  (Co(NH3)6H20)Br3  ;  (Co(NH3)1(H30)2)Br3  ; 
(Co(NH3)3(H20)3)Cl3  ;  (Co(NH3)6)Cl3  ;  (Co(NH3)6)(N02)3  ; 
(Cr(NH8)6)(N03)3. 

One  salt  giving  four  ions  had  the  molecular  conductivity 


10  COMPLEX   IONS 

522*9.     In  each  case  the  values  are  calculated  for  the  mole 
cule.     The  differences  between  the  values  for  the  different 
classes  are  so  large  that  the  method  may  be  usefully  applied 
to  determine  the  number  of  ions  formed   in   cases  where 
chemical  methods  fail  owing  to  analytical  difficulties. 

For  Werner's  method  of  classifying  these  compounds, 
and  numerous  references  to  original  papers  dealing  with 
them,  the  reader  is  referred  to  Werner's  Neuere  Anschauun- 
gen  auf  dem  Gebiete  der  Anorganischen  Ghemie  (Braunschweig, 
F.  Vieweg  und  Sohn,  1905),  or  the  English  translation,  New 
Ideas  on  Inorganic  Chemistry  (Longmans,  Green  &  Co.,  1911). 


CHAPTER   III 

THE  IONIC   MIGRATION   METHOD 

When  a  current  of  electricity  passes  through  an  electrolyte 
the  anions  and  kations  do  not,  in  general,  move  with  equal 
velocities.  Not  taking  account,  for  the  moment,  of  the  dis- 
charge of  the  ions  at  the  electrodes,  we  see  that  if  when  one 
f  araday  passes  through  the  solution  the  quantity  of  the  anion 
in  the  neighbourhood  of  the  anode  increases  by  x  gram- 
equivalents,  then  x  is  the  fraction  of  the  current  that  has 
been  carried  by  the  anions,  and  1  —  x  the  fraction  carried 
by  the  kations;  and  the  difference  between  the  total  quantities 
of  the  two  ion-forming  constituents,  including  the  portions 
discharged,  in  each  of  the  two  halves  of  the  cell  must  be  one 
equivalent.  By  analysing  the  solution  in  the  two  halves  of 
the  cell  after  passing  the  current  we  can  therefore  ascertain 
(1)  what  elements  are  present  in  the  anion  and  the  kation 
respectively,  and  (2)  the  quantities  of  these  elements  which 
are  contained  in  one  equivalent  of  the  anion  or  the  kation. 

Here,  then,  we  have  an  exact  and  unfailing  method  of 
recognising  the  formation  of  complex  ions  and  determining 
their  composition,  provided  that  only  one  kind  of  anions  and 
one  kind  of  kations  are  present,  i.e.  that  the  complex  formed 
is  a  fairly  stable  one. 

For  example,  if  we  pass  one  faraday  through  a  solution 
of  potassium  silver  cyanide,  we  shall  find  that  the  solution 
at  the  anode  contains  one  equivalent  of  silver  in  excess  of  the 
amount  corresponding  to  the  potassium  content.  The  solu- 
tion at  the  kathode  contains  two  equivalents  of  silver  less 
than  the  amount  corresponding  to  the  quantity  of  potassium 
present.  One  equivalent  of  silver  has  been  deposited  upon 
the  kathode,  so  that  including   the  discharged   silver  the 

u 


12  COMPLEX   IONS 

solution  has  lost  one  equivalent  of  silver  with  respect  to 
the  quantity  of  potassium  present.  The  silver  has  therefore 
migrated  to  the  anode  as  a  constituent  of  a  complex  ion,  and, 
further,  one  equivalent  of  this  complex  ion  contains  one 
equivalent  of  silver. 

The  ion  K>  is  the  only  kation  present,  and  bearing  in 
mind  that  the  algebraic  sum  of  the  negative  and  positive 
charges  in  the  solution  must  be  equal  to  nothing  and  that 
one  equivalent  of  the  complex  anion  contains  one  atom  of 
silver,  we  conclude  that  the  formula  of  the  complex  salt  must 
be  (KAg(CN)2)a;  and  that  it  must  split  into  the  ions  xK'  and 
(Ag(CN)2)a;,  having  as  negative  charges.  Molecular  weight 
determinations  (M.  Leblanc  and  A.  A.  Noyes,  Zeit.  phys. 
Chem.}  6,  395  (1890))  enable  us  to  decide  in  favour  of  the 
simple  formula  Ag(CN)2'  in  which  x  =  1. 

So  far  we  have  only  considered  the  relative  changes 
in  the  quantities  of  silver  and  potassium  present  in  the  two 
halves  of  the  cell.  By  comparing  these  quantities  with  those 
originally  present  we  can  calculate  the  migration  ratio  for  the 
anion  (x)  and  the  kation  (1  —  x).  If  the  complex  dissociates, 
then  in  a  series  of  measurements  with  solutions  of  different 
strengths  the  apparent  value  of  x,  the  migration  ratio  for 
the  complex  anion,  calculated  from  the  change  in  concentra- 
tion of  the  metal  it  contains,  will  evidently  diminish  with 
diminishing  concentration  of  the  solution,  since  more  and 
more  of  the  metal  functions  as  a  kation  instead  of  an  anion. 

In  the  years  1853-1859  Hittorf  {Fogg.  Annalen,  89,  177  ; 
98,  1 ;  103,  1 ;  106,  337,  513)  published  a  series  of  papers 
on  the  experimental  study  of  migration  in  solutions  of 
electrolytes  during  the  passage  of  a  current  through  them. 
His  method  was  the  one  which  is  still  often  used,  and 
consisted  in  passing  a  measured  quantity  of  electricity 
through  the  solution  and  analysing  the  liquid  in  the  neigh- 
bourhood of  the  anode  or  the  kathode. 

Hittorf  first  made  preliminary  experiments  with  copper 
sulphate  in  order  to  ascertain  whether  the  migration  ratio 
was  affected  by   the  current  density   in  the   solution,  and 


THE   IONIC   MIGEATION   METHOD 


13 


having  found  that  it  was  not  he  proceeded  to  study  the  effect 
of  concentration. 

The  following  salts  gave  almost  constant  values  for  the 
migration  ratio  in  solutions  of  concentration  below  0  "4N : 
CuS04,  AgN03,  Ag2S04,  AgC2H302,  KC1,  KBr,  KI,  K2S04, 
KN03,  KC2H302,  NH4CI,  NaCl,  NaN03,  NaC2H302. 

At  concentrations  above  0'4N"  the  transport  numbers  for 
some  of  the  salts  changed  with  the  concentration,  the  number 
for  the  anion  increasing  with  increasing  concentration. 
There  were  one  or  two  faintly  marked  exceptions  to  this  rule, 
where  the  number  changed  in  the  opposite  direction. 

Many  other  electrolytes,  however,  were  found  to  give 
quite  different  results  from  any  of  the  above  salts,  and 
notably  the  iodides  and  chorides  of  cadmium  and  zinc.  For 
example,  Hittorf  gave  the  following  figures  for  Cdl2  and 
CdCl2  :— 

Cadmium  Iodide. 


Transport  numbers. 

Temperature. 

Parts  water  to  one 
part  salt. 

Cd. 

L 

1-8313 

-0-258 

1-258 

11 

3-04 

-0-192 

1-192 

11-8 

4-277 

-0-148 

1-140 

11-2 

18-12 

0069 

0-931 

— 

69-60 

0-358 

0-642 

10 

166-74 

0-387 

0-613 

Cadmium  Chloride. 

Transport  numbers. 

Temperature. 

Parts  water  to  one 
part  salt. 

Cd. 

CI. 

10-6 

1-2724 

-0-015 

1-015 

9-8 

1-2692 

-0-016 

1-016 

6-8 

1-2848 

-0-014 

1-014 

7 

1-9832 

0-127 

0-873 

9-6 

2-7588 

0-221 

0-779 

9-5 

3-3553 

0-228 

0-772 

? 

5-7611 

0-256 

0-744 

7-8 

98-708 

0-275 

0-725 

10-5 

191-82 

0-292 

0-708 

14  COMPLEX  IONS 

Hittorf  also  studied  potassium  ferrocyanide,  potassium 
silver  cyanide,  sodium  platinichloride,  potassium  aurichloride, 
and  the  salts  HgCl2>  2KC1,  2HgCl2,  2KC1,  4HgCl2,  2KC1 
and  Cdl2,  2KI,  and  showed  that  in  each  case  the  alkali  metal 
forms  the  kations  and  moves  towards  the  kathode,  while  a 
portion  of  the  nobler  metal  moves  with  the  acid  radicle 
towards  the  anode.  In  the  cases  of  potassium  ferrocyanide, 
potassium  silver  cyanide,  and  sodium  platinichloride  the 
gain  in  the  metal  of  the  anion  at  the  anode  or  the  loss  at  the 
kathode  compared  with  the  amount  of  alkali  metal  present 
was  exactly  an  integral  number  of  equivalents  for  each 
equivalent  of  silver  deposited  in  the  voltameter  in  series 
with  the  cell,  showing  that  the  salt  split  solely  into  kations 
of  the  alkali  metal  and  complex  anions  containing  the 
nobler  metal. 

In  the  case  of  potassium  aurichloride  and  the  other  salts 
mentioned  above  the  loss  at  the  kathode  was  less  than  would 
have  been  the  case  had  the  complex  ion  been  quite  stable, 
and  Hittorf  therefore  concluded  that  dissociation  had 
occurred,  and  according  to  the  theory  of  the  time  this  was 
supposed  to  be  due  to  the  influence  of  the  electric  current. 

In  order  to  make  the  foregoing  clearer  we  shall  consider 
two  numerical  examples  from  Hittorf. 

1 .  Potassium  ferrocyanide. 

13*7207  grams  of  solution  before  electrolysis  gave  2*0505 
grams  of  potassium  sulphate  and  0*4769  gram  of  ferric 
oxide.  23*3087  grams  of  solution  from  the  anode  chamber 
after  electrolysis  gave  3*2445  grams  of  potassium  sulphate 
and  0*8586  gram  of  ferric  oxide.  During  the  passage  of  the 
current  0*5625  gram  of  silver  was  deposited  on  the  kathode 
in  the  voltameter. 

Using  Hittorf  s  values  for  the  equivalents  we  find  that 
the  anode  solution  after  electrolysis  contained  1*4585  grams 
of  potassium  and  0*60096  gram  of  iron.  In  potassium 
ferrocyanide  1*4585  grams  of  potassium  are  equivalent  to 
0*5209  gram  of  iron,  or,  taking  the  figures  from  the  analysis 
of  the  solution   before   electrolysis,    0*5281   gram   of  iron. 


THE  IONIC   MIGEATION  METHOD  15 

There  was  thus  an  excess  of  iron  in  the  anode  chamber  over 
the  amount  corresponding  to  the  amount  of  potassium  present 
of  0-60096  -  0-5281  gram,  =  0*07286  gram  =0-002602 
equivalent.  The  reduced  silver,  0'5625  gram,  is  0*00521 
equivalent.  It  follows,  therefore,  that  the  valency  of  an  ion 
containing  one  equivalent  of  iron  is  0-00521/0-002602,  or  the 
valency  of  the  complex  ion  containing  one  atom  of  iron  is 
2  x  0*00521/0-002602  =  4,  almost  exactly. 

Similarly,  the  deficit  in  potassium  corresponding  to  two 
equivalents  of  iron  is  four  gram  atoms.  Hence,  if  the  complex 
ion  is  not  associated,  its  formula  must  be  Fe(CN)6"",  and  the  salt 
on  dissociation  yields  this  complex  anion  and  four  potassium  ions . 

Further,  we  may  calculate  the  transport  numbers  for  the 
anion  and  the  kation  in  the  usual  way.  Before  electrolysis, 
13*7207  grams  of  the  solution  contained  1*5341  grams  of 
KCN  and  0*644  gram  of  Fe(CN)2.  After  electrolysis, 
23*3087  grams  of  the  anode  solution  contained  2*4282  grams 
of  KCN  and  1*1591  grams  of  Fe(CN)2.  No  gas  is  produced 
at  the  anode  until  all  the  Fe(CN)6""  has  been  oxidised 
to  Fe(CN)6'",  when  oxygen  begins  to  be  evolved.  The  elec- 
trolysis was  stopped  as  soon  as  the  first  bubbles  of  oxygen 
were  seen,  and  the  amount  of  cyanogen  in  addition  to  that 
included  in  the  above  weights  of  KCN  and  Fe(CN)2  was 
calculated  from  the  weight  of  silver  deposited  in  the 
voltameter.  Its  weight  is  0*5625  x  T%6¥  =  0*1353  gram.  The 
anode  solution  therefore  contains  23*3087  -  2*4282  -  1*1591 
-  0*1353  =  19*5861  grams  of  water. 

Before  electrolysis  this  amount  of  water  would  have 
corresponded  to  1*5641  grams  of  potassium,  so  that  the 
loss  of  potassium  is  1*5641  —  1*4585  =  0*1056  gram.  The 
weight  of  potassium  corresponding  to  0*5625  gram  of  silver 
is  0*204  gram.  We  thus  find  that  the  transport  number  for 
the  kation  (K-)  is  0*1056/0*204  =  0*518,  while  similarly  that 
for  the  anion  is  0*482. 

2.  Potassium  cadmium  iodide. 

This  salt  has  the  composition  which  is  represented  by  the 
formula  K2CdI4. 


16  COMPLEX   IONS 

The  solution  was  prepared  by  dissolving  equivalent 
amounts  of  cadmium  iodide  and  potassium  iodide  in  a  small 
quantity  of  water.  15*8994  grams  of  solution  gave  16*102 
grams  of  silver  iodide,  3*4367  grams  of  potassium  nitrate,  and 
2-223  grams  of  cadmium  oxide.  24*6033  grams  of  solution 
from  the  kathode  vessel  after  electrolysis  gave  24*6147  grams 
of  silver  iodide,  6*2027  grams  of  potassium  nitrate,  and  2*8352 
grams  of  cadmium  oxide.  During  electrolysis  0*9784  gram 
of  silver  was  deposited  in  the  voltameter. 

In  the  original  solution  6*2027  grams  of  potassium  nitrate 
would  correspond  to  3*4833  grams  of  cadmium,  while  the 
amount  of  cadmium  found  was  2*4808  grams.  The  deficit 
of  cadmium  is  therefore  3*4833  -  2*4808  =  1*0025  grams 
cadmium,  or  0*0179  equivalent.  The  silver  deposited  in  the 
voltameter  was  0*00906  equivalent,  and  this  amount  of 
cadmium  was  also  deposited  upon  the  kathode.  The  deficit 
due  to  migration  was  therefore  0*0179  -  0*00906  =  0*00884 
equivalent. 

Thus  the  cadmium  moved  towards  the  anode  during  the 
electrolysis,  and  if  it  all  behaved  alike,  the  valency  of  the 
ion  containing  an  atom  of  cadmium  (two  equivalents)  was 
0*00906/0*00884  x  i  =  2*05.  The  salt  thus  forms  the  ions 
2K*  and  Cdl4".  The  same  result  may  be  obtained  by 
calculating  from  the  quantities  of  silver  iodide  and  cadmium 
oxide  or  from  the  silver  iodide  and  potassium  nitrate  found. 

Calculating  the  migration  ratios  as  before,  we  find — 

uA  (ratio  for  the  anion)  =0*31 

uK  (ratio  for  the  kation  by  difference)  =  0*69 

It  is  interesting  to  calculate  the  fraction  of  the  current 
carried  by  each  constituent  of  the  solution.  We  may  carry 
this  out  as  follows  : — 

15*899  grams  of  the  original  solution  contained  5*645 
grams  of  potassium  iodide  and  6*343  grams  of  cadmium 
iodide,  and  hence  3*911  grams  of  water.  The  cadmium  con- 
tent of  this  solution  is  1*946  grams. 

24*6033  grams  of  the  kathode  solution  after  electrolysis 


THE  IONIC   MIGEATION  METHOD  17 

contained  8086  grams  of  cadmium  iodide,  10*188  grams  of 
potassium  iodide,  and  hence  6*329  grams  of  water.  The 
cadmium  content  of  this  solution  was  2*482  grams. 

6*329  grams  of  water  in  the  original  solution  corresponds 
to  3*149  grams  of  cadmium.  Hence  the  decrease  in  the  cad- 
mium content  of  the  kathode  solution  compared  with  the 
original  solution  is  3*149 -2-481  =  0*668  gram  or  0*01189 
equivalent. 

0*00906  equivalent  of  cadmium  was  deposited  upon  the 
kathode,  so  that  the  loss  due  to  migration  was  0*01189 
-0*00906=0*00283  equivalent. 

Thus  the  migration  ratio,  assuming  the  cadmium  to  be 
positively  charged,  is  -0*00283/0*00906=  -0*312. 

Similarly,  the  values  for  the  iodine  and  potassium 
respectively  are  0*613  and  0*712. 

These  figures  really  represent  the  fractions  of  the  current 
that  travel  in  company  with  the  respective  constituents 
through  the  solution.  Comparing  the  values  for  cadmium 
and  iodine,  we  see  that  the  ratio  for  iodine  is  almost  exactly 
double  that  for  the  cadmium,  showing  that  the  two  equiva- 
lents of  iodine  accompany  each  equivalent  of  cadmium,  or, 
in  other  words,  that  the  formation  of  the  ion  Cdl4"  is  prac- 
tically complete. 

In  more  dilute  solutions  the  behaviour  was  less  simple. 
Thus,  in  a  solution  containing  one  part  of  the  salt  to  58*72 
parts  of  water,  Hittorf  found  the  migration  ratios 

Iodine 0*560 

Cadmium 0*00 

Potassium 0*459 

so  that  the  cadmium  had  apparently  not  moved  at  all,  or 
different  portions  of  it  had  moved  in  opposite  directions. 
Hittorf  therefore  concluded  that  the  "  double  salt "  dissociated 
as  the  dilution  increased.1 

It  is  worthy  of  remark  that  these  results  were  arrived  at 

1  McBain  (Zeit.  Elektrochem.,  11,  222  (1905))  has  shown  that  iu  weaker 
solutions  the  ion  Cdl3'  is  formed. 

C 


18  COMPLEX   IONS 

in  days  when  no  word  had  been  heard  of  the  modern  theory 
of  electrolytic  dissociation,  and  before  any  quantitative  ex- 
pression had  been  found  for  the  law  of  mass  action. 

In  later  years  more  exact  measurements  of  migration 
ratios  were  made,  and  subsequently  methods  were  invented 
by  which  the  speed  of  the  ions  could  be  directly  observed* 

Thus  A.  A.  Noyes  {Technology  Quarterly,  17,  4,  Dec, 
1904)  made  very  exact  measurements  of  the  migration  ratios 
for  the  following  salts :  KC1,  NaCl,  HC1,  HN03,  AgN03, 
Ba(N02)2,  K2S04,  CuS04,  LiCl,  CdS04,  BaCl2,  and  the 
halides  of  several  other  divalent  metals.  For  the  eight  salts 
first  mentioned  the  ratio  does  not  change  to  the  extent  of 
one  per  cent,  of  its  value  while  the  concentration  is  increased 
from  0'02N  to  TON.  In  the  solutions  of  LiCl,  CdS04, 
BaCl2,  and  other  chlorides  of  the  heavy  metals,  the  ratio  for 
the  anion  increases  with  increasing  concentration. 

Direct  measurements  of  the  velocity  of  a  number  of  ions 
have  been  made  by  Whetham  {Phil.  Trans.,  A,  1893,  337), 
Masson  {Zeit.  phys.  Ghemie,  29,  501  (1899)),  Steele  (Zeit.phys. 
Chemie,  40,  689  (1902)),  and  others.  Whetham  and  Masson 
worked  with  solutions  in  jellies,  but  Steele  succeeded  in  dis- 
pensing with  the  jelly.  The  effect  of  the  gelatine  upon  the 
velocity  is  small.  The  results  of  these  measurements  showed 
that  the  velocity  is  only  completely  independent  of  the  con- 
centration in  the  case  of  a  few  salts,  but  in  the  cases 
mentioned  above  the  variation  is  only  slight. 

All  succeeding  work  has  tended  to  ratify  the  general 
results  of  the  rather  less  refined  experiments  of  Hittorf. 

The  interpretation  of  the  variability  of  the  ionic  velocities 
has  been  the  subject  of  much  controversy.  Noyes  pointed 
out  that  a  disturbing  influence,  such  as  alteration  in  the  ionic 
friction  with  change  in  concentration  which  changes  the 
velocity  of  one  ion,  should  also  change  that  of  the  other  to 
about  the  same  extent,  and  thus  be  nearly  without  effect 
upon  the  ratio.  He  therefore  concluded  that  the  only  pos- 
sible cause  of  variability  in  the  ratio  was  the  formation  of 
complex  ions.     Steele  {Phil.   Trans.,   A,    1902,    105)   in   a 


THE   IONIC   MIGRATION   METHOD  19 

review  of  the  whole  subject  of  migration  in  relation  to  com- 
plex formation  came  to  the  same  conclusion. 

On  the  other  hand,  Riesenfeld  and  Reinhold  (Zeit.  phys. 
Chemie,  66,  672)  consider  the  variation  in  the  migration 
ratio  to  be  due  to  hydrate  formation. 

Without  entering  into  a  discussion  of  the  subject  it  may 
be  said  that  change  in  the  degree  of  hydration  of  the  ions 
does  probably  cause  small  deviations  from  constancy  in  the 
migration  ratio,  but  that  this  does  not  affect  the  conclusions 
that  have  been  drawn  from  the  study  of  migration  in  the 
case  of  comparatively  stable  complexes. 

The  bearing  of  the  hydrate  theory  in  general  upon  the 
theory  of  complex  ions  will  be  discussed  in  Appendix  I. 


CHAPTEE  IV 

THE  DISTRIBUTION  METHOD 

When  a  substance  dissolves  in  two  very  slightly  miscible 
liquids  in  contact  with  one  another  the  ratio  of  the  con- 
centrations of  molecules  of  the  same  kind  in  the  two  layers 
is  constant.  This  was  shown  experimentally  for  various 
substances  by  Berthelot  and  Jungfleisch  (Ann.  chim.  phys., 
(4)  26,  396  (1872)),  and  may  be  proved  theoretically  by 
considering  the  case  in  which  the  solute  is  a  gas  (see,  for 
example,  Nernst,  Theoretische  Chemie,  5te  Auflage,  p.  490). 
When  the  two  layers  are  in  equilibrium  the  gaseous  pressure 
of  the  solute  in  the  surrounding  space  must  be  the  same  for 
both.  This  pressure  is  proportional  to  the  concentration  in 
each  solvent,  so  that  if  the  gaseous  pressure  be  p  and  the 
concentrations  c\  and  c2  we  have 

p  =  ktfi  =  k2c2 

and  hence  —  =  =-  =  constant 

c2       K\ 

This  relation  holds  goods  for  every  kind  of  solute  mole- 
cules that  may  be  present,  and  for  each  kind  it  is  inde- 
pendent of  the  others. 

Thus,  if  a  substance  dissolves  to  a  measurable  extent  in 
the  two  liquids  but  consists  mainly  of  different  molecules  in 
the  two  layers,  the  total  concentrations  are  no  longer  pro- 
portional to  one  another.     In  this  case,  as  before, 

d  =  kc% 

when  ci  and  c2  represent  the  concentrations  of  molecules  of 
one  kind.     Suppose  that  in  the  liquid   (2)    the  substance 

20 


THE  DISTRIBUTION  METHOD  21 

exists  mainly  in  the  form  of  double  molecules :   we  then 
obtain  from  the  law  of  mass-action 

e22  =  k'c3 
where  c3  is  the  concentration  of  double  molecules.     If  the 
amount  of  substance  present  as  single  molecules  is  small 
(i.e.  if  h'  is  small)  the  concentration  as  determined  analyti- 
cally is  practically  c3,  and  we  thus  find 

cx  =  h\Zk'c3  =  KVC3 

Thus  Nernst  (Zeit.  phys.  Chem.y  8,  110  (1891))  determined 
the  distribution  coefficient  of  benzoic  acid  between  water 
and  benzene  at  various  concentrations,  and  found  that  the 
concentration  in  the  water  layer  was  proportional  to  the 
square  root  of  the  concentration  in  the  benzene  layer, 
showing  that  the  benzoic  acid  in  the  benzene  consisted 
mainly  of  double  molecules,  in  agreement  with  the  freezing- 
point  determinations  of  Beckmann  (Zeit.  phys.  Ghem.,  2,  729 
(1888)).  Beckmann's  results  indicated  a  slight  dissociation 
into  single  molecules  in  weak  solutions,  and  the  distribution 
experiments  showed  the  same  result.  Since  benzoic  acid 
dissociates  electrolytically  to  a  small  extent  in  the  water 
layer  the  amount  of  dissociated  acid  must  be  subtracted  from 
the  total  amount  in  order  to  obtain  the  true  concentration  of 
undissociated  molecules.  Various  other  substances  were 
examined  by  Nernst  in  this  way,  and  in  each  case  the  re- 
sults were  in  agreement  with  those  obtained  by  the  freezing- 
point  methods. 

Again,  if  we  know  the  distribution  ratio  of  a  substance 
between  two  liquids  and  find  that  it  apparently  changes  on 
introducing  a  small  quantity  of  a  solute  which  dissolves 
only  in  one,  we  are  able  to  conclude  that  the  two  solutes 
form  a  compound,  and  we  can  tell  how  much  of  the  first  one 
has  combined  with  the  second.  This  method  has  been  used 
for  the  investigation  of  certain  cases  of  complex  formation. 

Thus  Koloff  (Zeit.  phys.  Chem.,  13,  341  (1894))  studied 
the  reaction  which  occurs  in  aqueous  solution  between 
bromine  and  potassium  bromide,  by  shaking  various  solutions 


22  COMPLEX   IONS 

of  potassium  bromide  with  a  strong  solution  of  bromine 
in  carbon  disulphide.  A  sufficiently  large  quantity  of  this 
solution  was  used  to  ensure  that  the  change  in  its  con- 
centration due  to  the  withdrawal  of  bromine  by  the  potassium 
bromide  solutions  should  be  small.  The  solution  was  first 
shaken  with  water,  and  the  concentration  of  bromine  in  the 
water  layer  determined.  The  successive  solutions  of  potas- 
sium bromide  were  then  shaken,  the  amount  of  bromine  in 
the  water  layer  being  found  by  titration  in  each  case. 
Finally,  the  carbon  disulphide  solution  was  shaken  with 
water  again,  and  the  change  in  the  amount  of  bromine 
withdrawn  noticed. 

From  the  quantities  of  bromine  in  the  water  layer  in  the 
first  and  last  experiments  the  concentrations  of  free  bromine 
in  the  potassium  bromide  solutions  were  obtained  by  inter- 
polation, the  amount  removed  in  each  experiment  being 
known.  Calling  these  concentrations  D  and  the  concentra- 
tions found  by  titration  B,  it  follows  that  in  any  experiment 
B  —  D  gram  molecules  per  litre  have  reacted  to  form  a  com- 
plex with  the  potassium  bromide.  Thus  by  this  method  it 
was  unnecessary  to  determine  the  distribution  ratio,  and  the 
awkward  determination  of  bromine  in  a  strong  carbon 
disulphide  solution  was  avoided. 

In  order  to  calculate  the  dissociation  constant  of  the 
complex  ion  we  must  adopt  a  hypothetical  scheme  repre- 
senting the  reaction ;  and  conversely,  since  the  complex  ion 
must  have  a  dissociation  constant,  it  follows  that  if  the  law 
of  mass-action  holds  good  the  scheme  which  gives  constant 
values  for  the  dissociation  constant  is  the  one  which  truly 
represents  the  reaction. 

Eoloff  proceeded  to  calculate  the  dissociation  constant  for 
the  complex  ion  on  the  assumption  that  it  had  the  constitu- 
tion Br3',  and  found  constant  values  for  the  dissociation 
constant.  On  this  hypothesis  the  reaction  between  the 
bromine  ion  and  the  molecule  of  bromine  must  be  repre- 
sented by  the  equation 

Br3'  =  Br2  +  Br' 


THE  DISTRIBUTION  METHOD 


23 


whence  we  obtain 

[Br3']  =  K[Br2][Br'] 

Calling  the  initial  concentration  of  bromine  ions  A  we 
have 

[Br3'j  =  B  -  D 

[Br2]  =  D 

[Br'J   =  A  -  (B  -  D) 

This  calculation  does  not  take  account  of  the  electrolytic 
dissociation  of  the  potassium  bromide.  We  are  assuming 
either  (1)  that  the  electrolytic  dissociation  is  complete, 
which  is  not  far  from  the  actual  state  of  affairs,  or  (2)  that 
the  Br2  molecules  combine  equally  well  with  the  bromine 
ions  and  with  the  undissociated  potassium  bromide. 
Further,  the  undissociated  complex  salt,  if  any,  must  behave 
like  the  complex  ion.     We  thus  obtain 

D(A  -  (B  -  D)) 


K  = 


B  -  D 


Using  these  expressions  the  following  values  were  found  :- 


Temperature  =  32-6°  C. 


D. 

B. 

A. 

K. 

00264  (water) 
00261 
00259 
00257 
0-0255  (water) 

01111 
0-0686 
0-0472 

- 

0-250 
0-125 
0-0625 

0-0508 
0-0500 
0-0488 

Temperature  : 

=  32-7°  C. 

D 

B. 

A. 

K. 

00318  (water) 
00316 
00315 
00313 
0-0312  (water) 

0-1273 
00795 
0-0555 

0-250 
0-125 
00625 

00510 
0-0505 
00498 

Another  set  of  measurements  was  made  in  which  the 


24 


COMPLEX  IONS 


concentration  of  the  bromine  was  altered  by  adding 
measured  quantities  of  carbon  disulphide  while  the  potas- 
sium bromide  concentration  remained  constant.  The 
results  are  given  below. 


Tempeeatdre  =  32-6°  C. 


D. 

B. 

A. 

K. 

0-0477  (water) 

_ 



_ 

00475 

0-1078 

0125 

00510 

00236 

0-0646 

0-125 

0-0501 

00157 

00452 

0-125 

0-0508 

0-0117 

00362 

0125 

00480 

0-0116  (water) 

— 

— 

— 

It  is  thus  clear  that  the  scheme 


Br«' 


Br2  +  Br' 

must  be  taken  as  representing  very  closely  the  real  state  of 
affairs. 

Eoloff  concluded  that  the  free  bromine  must  attach 
itself  to  the  undissociated  potassium  bromide,  as  well  as  to 
the  bromine  ions.  As  the  salt  is  nearly  completely  dis- 
sociated this  has  little  bearing  upon  the  formation  of  the 
complex  ion  as  deduced  from  the  results.  This  work,  there- 
fore, affords  very  strong  evidence  of  the  formation  of  the 
complex  ion  Br3',  and  also  gives  us  information  as  to  its 
stability. 

Further  experiments  on  the  subject  were  made  by 
Worley  (Trans.  Chem.  Soc,  87,  1107  (1905)),  who  deter- 
mined the  solubility  of  bromine  in  solutions  of  potassium 
bromide,  and  also  measured  the  concentration  of  free  bromine 
in  unsaturated  solutions  by  getting  the  solutions  into  equili- 
brium with  a  quantity  of  water  separated  from  the  solution 
by  an  air-space  which  was  partially  evacuated.  In  each 
case  the  results  showed  that  in  weak  solutions  the  compound 
KBr3  was  formed,  while  in  more  concentrated  solutions 
small  quantities  of  a  higher  poly  bromide  were  present. 


THE  DISTRIBUTION  METHOD  25 

The  distribution  method  was  also  employed  by  Jakowkin 
(Zeit.  phys.  Chem.,  13,  539  (1894)  ;  18,  585  (1895) ;  20,  19 
(1896))  in  investigating  the  complex-formation  in  solutions  of 
iodine  in  potassium  iodide.  Jakowkin  measured  the  distri- 
bution of  iodine  between  water  and  carbon  disulphide  and 
determined  the  iodine  in  the  carbon  disulphide  layer  in 
contact  with  the  complex  solution.     The  constant 

[KI][IJ 
[KI3] 

calculated  from  his  first  results  varied  somewhat  with  the 
concentrations  of  the  components.  Further  experiments 
showed,  however,  that  the   distribution  ratio  is  not  quite 

independent  of  the   concentrations,  the   ratio  ^^-  rising 

U(H20) 

as  the  concentration  increases.  This  indicated  that  associa- 
tion occurs  to  some  extent  in  the  carbon  disulphide  layer. 
The  values  of  the  distribution  constant  were  therefore  plotted 
against  the  concentration,  so  that  the  free  iodine  in  the 
aqueous  layer  could  be  calculated  with  accuracy  from  the 
concentration  in  the  carbon  disulphide  layer.  On  making 
this  correction  thoroughly  concordant  values  were  obtained 
for  the  constant  over  a  wide  range  of  concentrations.  Nearly 
the  same  value  was  obtained  with  solutions  of  lithium, 
sodium,  and  barium  iodides.  Hydriodic  acid  solutions  gave 
a  slightly  lower  value. 

These  experiments  thus  show  that  the  compound  KI3  is 
formed  in  solutions  of  iodine  and  potassium  iodide,  and  this 
dissociates  yielding  the  complex  ion  I8\  In  the  light  of  this 
knowledge  such  solutions  were  used  by  Abegg  and  Maitland 
(Zeit.  Mektrochemie,  12  (1906))  in  order  to  measure  the 
electrolytic  potential  of  iodine. 

It  may  be  noted  that,  as  in  the  case  of  RolofFs  work, 
Jakowkin  assumes  that  the  iodine  ion  and  the  undissociated 
potassium  iodide  act  similarly. 

Jakowkin  also  repeated  RolofFs  work  with  potassium 
bro  mide  and  bromine,  using  carbon  tetrachloride  in  place  of 


26  COMPLEX   IONS 

carbon  disulphide,  and  found  concordant  values  for  the 
constant 

_    [KBr][Br2] 

~       [KBr3] 

the  values  being  a  little  higher  than  BolofFs.  He  also 
studied  the  equilibria 

NaCl  +  I2^NaClI2 

KCl  +  Br2^KClBr2 

KBr-f  l2^KBrT2 

and  in  each  case  the  experimental  results  showed  satisfactory 
agreement  with  the  law  of  mass-action  in  accordance  with  the 
above  schemes,  thus  showing  the  existence  of  the  ions  C1I2', 
ClBr2',  Brl2'. 

When  the  concentration  of  the  dissolved  salt  is  consider- 
able it  exerts  an  appreciable  effect  upon  the  solubility  of  the 
free  halogen,  and  hence  upon  the  distribution  coefficient, 
which  is  the  ratio  of  the  solubilities  in  the  two  solvents.  This 
effect  was  studied  by  Setschenoff  (Zeit.  phys.  Chem.,  4,  117 
(1889)),  and  the  concentrations  obtained  using  the  distribu- 
tion coefficient  were  corrected  in  accordance  with  the 
expression  worked  out  by  him.  It  was  found,  however,  that 
when  the  concentration  of  the  halogen  was  largely  increased 
the  values  of  the  dissociation  constant  fell  somewhat. 

The  only  explanation  that  could  be  offered  for  this  was 
that  higher  poly  iodides  are  formed.  Wildermann  (Zeit.  phys. 
Chem.,  11,  407  (1893))  arrived  at  the  same  conclusion  from 
a  study  of  the  solubility  of  bromine  in  potassium  bromide 
solutions. 

A  very  large  number  of  solid  tri-halides  of  the  alkali 
metals  has  been  obtained  including  both  simple  and  mixed 
salts  (Johnson,  Trans.  Chem.  Soc.,  31,  249  (1877);  Wells 
and  Penfield,  Zeit.  anorg.  Chem.,  1,  85  (1892) ;  Wells  and 
Wheeler,  ibid.,  1,  442  (1892)),  and  numerous  examples  of 
the  formation  of  polyiodides  of  organic  bases  are  known. 
Further,  Wells  and  Wheeler  (loc.  cit.)  obtained  the  solid 
compounds  Csls,  CsBr5,  etc.,  and  later  Abegg  and  Hamburger 


THE   DISTRIBUTION   METHOD  27 

(Zeit.  anorg.  Chem.,  50,  403  (1906))  prepared  numerous 
polyiodides  of  ammonium  and  the  alkali  metals,  the  two 
containing  the  largest  possible  amount  of  iodine  at  25°  being 
Rbl9  and  Csl9.  Dawson  and  his  co-workers  (Dawson  and 
Gawler,  Trans.  Chem.  Soc.,  81,  524  (1902)  ;  Dawson  and 
Goodson,  ibid.,  85,  796  (1904);  Dawson,  ibid.,  85,  467 
(1904))  showed  the  existence  of  a  similar  series  of  compounds 
in  solution  in  nitrobenzene  and  other  organic  solvents,  the 
composition  of  the  compounds  in  the  solutions  being  arrived 
at  by  means  of  distribution  experiments. 

The  distribution  method  was  also  used  by  Dawson  and 
McCrae  (Trans.  Chem.  Soc.,  1901,  496,  1072)  in  order  to 
examine  the  constitution  of  the  cuprammonium  ion  in 
solution.  The  distribution  coefficient  for  ammonia  between 
water  and  chloroform  was  first  determined.  This  is  nearly 
independent  of  the  concentration,  but  shows  a  very  slight 
variation.  To  correct  for  this  the  coefficient  was  found  by 
interpolation  for  each  concentration  used.  Thus  by  measur- 
ing the  concentration  of  ammonia  in  the  chloroform  layer 
the  concentration  of  free  ammonia  in  the  aqueous  layer 
was  calculated.  The  total  amount  of  ammonia  in  both  layers 
being  known,  the  quantity  of  "  fixed "  ammonia  in  the 
aqueous  layer  was  found,  and  hence  the  number  of  molecules 
of  ammonia  which  were  combined  with  each  molecule  of 
copper  salt.  Experiments  with  copper  sulphate  at  10°  C. 
and  at  30°  C.  respectively  showed  that  in  each  case  this 
number  was  about  3*6.  The  true  number  must  obviously 
be  an  integer,  and  Dawson  and  McCrae  considered  the 
most  probable  explanation  to  be  that  the  salt  CuS04,  4NH3 
is  formed,  and  undergoes  partial  dissociation. 


CHAPTEK  V 

THE  SOLUBILITY  METHOD 

When  a  binary  electrolyte  is  dissolved  in  water  the  molecules 
dissociate  in  the  solution  according  to  the  scheme 
AB^A'+B- 

where  AB  represents  the  undissociated  molecule  of  salt,  A' 
the  negatively  charged  ion,  and  B*  the  positively  charged  one. 
If  we  keep  on  adding  solid  salt  to  the  liquid  a  stage  is 
finally  reached  when  no  more  solid  will  dissolve,  and  the 
solution  is  saturated  with  the  salt.  This  state  of  affairs  is 
determined  by  the  equilibrium 

AB  (solid)  ^  AB  (dissolved) 

and  the  system  has  two  degrees  of  freedom,  the  vapour 
phase  being  absent.  At  a  given  temperature  and  pressure, 
therefore,  the  concentration  of  AB  molecules  in  the  solution 
is  fixed  if  the  solid  salt  is  present.  The  effect  of  changes  in 
the  pressure  of  the  atmosphere  upon  the  solubility  of  a  salt 
is  negligible,  so  that  practically  the  saturation  concentration 
of  undissociated  molecules  is  affected  only  by  temperature. 

In  a  saturated  solution  the  concentrations  of  the  ions 
A'  and  B*  must  be  such  that 

*[A1B-]  =  [AB] 
so  that  in  a  saturated  solution  the  product  [A'][B*]  is  also 
constant.     This  product  is  called  the  Solubility  Product. 

The  solubility  of  a  salt  in  water  is  therefore  made  up  of 
two  parts,  namely,  (1)  the  concentration  of  the  undissociated 
molecules,  and  (2)  the  concentration  of  one  of  the  ions 
produced  from  them. 


THE   SOLUBILITY   METHOD  29 

If  to  a  saturated  solution  of  an  electrolyte  another 
electrolyte  be  added,  having  one  ion  (A')  in  common  with 
the  first,  without  altering  the  volume  of  the  solution,  the 
value  of  [A']  tends  to  be  increased.  This  causes  some  of 
the  ions  A'  to  combine  with  the  ion  B*  forming  undissociated 
salt  molecules,  AB.  This  in  its  turn  is  precipitated,  since 
the  solution  is  already  saturated  with  respect  to  AB.  The 
total  result  is  therefore  that  the  solubility  of  an  electrolyte 
is  lowered  by  adding  to  the  solution  a  second  electrolyte 
having  one  ion  in  common  with  the  first  electrolyte. 

We  shall  now  proceed  to  calculate  the  solubility  of  a 
slightly  soluble  electrolyte  in  a  solution  previously  contain- 
ing a  second  electrolyte  at  a  given  concentration,  containing 
an  ion  in  common  with  the  first  electrolyte.  This  calculation 
was  first  worked  out  and  applied  by  Nernst. 

Let  s  be  the  solubility  of  the  slightly  soluble  electrolyte 
in  water,  7  its  degree  of  dissociation  in  saturated  solution, 
and  x  the  concentration  of  the  common  ion  in  the  added 
electrolyte — that  is,  the  electrolyte  already  in  the  solution. 
If  this  is  a  highly  dissociated  substance  the  value  of  the 
constant 

[AB] 

will  be  high,  and  a  small  change  in  [AB]  will  correspond  to 
a  large  alteration  in  the  value  of  [A']  or  [B*].  Thus  the 
addition  of  a  relatively  small  amount  of  the  (slightly  soluble) 
electrolyte  producing  either  A'  or  B*  ions  will  not  materially 
affect  the  degree  of  dissociation  of  the  added  electrolyte,  so 
that  in  the  mixed  solution  we  may  take  the  concentration  of 
either  ion  due  to  this  electrolyte  as  equal  to  x  without  serious 
error. 

If  71  be  the  degree  of  dissociation  of  the  slightly  soluble 
salt  in  the  mixed  solution  which  is  saturated  with  it,  and 
r)  its  solubility,  i.e.  its  concentration  in  this  solution,  we 
have 

711  (Yil  +  x)  =  O7)2 


30 


COMPLEX   IONS 


Solving  for  »j  we  obtain 


t]  =  - 


(1) 


This  is  the  original  formula  of  Nernst.  The  equation,  how- 
ever, contains  two  unknown  quantities,  71  and  rj.  From  the 
values  of  7  and  s  for  the  water  solution  it  is  possible  to  find 
approximately  the  value  of  71,  and  so  to  calculate  tj. 

This  method  was  tested  experimentally  by  A.  A.  Noyes 
(Zeit.  phys.  Chem.,  6,  241  (1890)),  who  determined  the  solu- 
bility of  silver  bromate  in  solutions  of  silver  nitrate  and 
potassium  bromate  respectively.  The  following  table  gives 
the  values  found  by  Noyes : — 


Cone,  of  added 
salt. 

Solubility  of 
AgBr03inAgN03. 

Solubility  of 
AgBr03  in  KBr03. 

Solubility 
calculated . 

0 

0-00850 

00346 

0-00810 
0-00510 
0-00216 

0-00810 
000519 
0-00227 

000504 
0-00206 

The  agreement  between  the  observed  values  and  those  calcu- 
lated from  the  equation  is  quite  good,  and  as  the  determina- 
tion of  71  was  accomplished  by  means  of  a  rather  inexact 
extrapolation  the  small  differences  may  be  due  to  error 
introduced  in  this  way. 

A  simpler  and  more  exact  method  of  performing  the 
calculation  is  the  following,  which  was  worked  out  and  used 
by  the  author  {Trans.  Faraday  Soc,  5,  225  (1910))  in  calcu- 
lating the  solubility  of  silver  acetate  in  silver  nitrate  and 
sodium  acetate  solutions. 

Solving  the  equation 

ymiyiri  +  x)  =  (s7)2 
for  yiTj  instead  of  for  rj  we  obtain 


v? 


+  (*r)2 


Now,  since   the  solubility  »i  is   made  up   of  the   constant 


THE   SOLUBILITY   METHOD 


31 


concentration  of  the  undissociated  salt  which  is  given  by 
s(l  —  y)  and  the  concentration  of  the  ion  which  is  not 
common  to  the  two  salts,  namely,  ym,  we  have 

7]  as  8(1  -  y)^  +  yirj 

Substituting  the  value  of  yxt)  in  this  equation,  we  find 


1=  -|  +  \/J+(Sy)2  +  S(l  -7)       .     (2) 

We  thus  obtain  17  in  terms  of  x,  s,  and  7,  all  of  which  can  be 
accurately  determined. 

The  following    table    shows    the   values   obtained    by 
recalculating  Noyes'  results  in  this  way  : — 


Cone,  of  added 
salt. 

Solubility  of 
AgBr03inAgN03. 

Solubility  of 
AgBr03inKBr03. 

Calculated 
solubility. 

0 

0-00850 

00346 

0-00810 
0-00510 
0-00216 

0-00810 
0-00519 
0-00227 

000510 
0-00223 

The  agreement  is  thus  improved  by  using  formula  (2).  The 
author  also  found  good  agreement  between  the  calculated 
experimental  values  in  the  case  of  solutions  of  silver  acetate 
in  silver  nitrate. 

Noyes  also  showed  that  it  follows  from  the  law  of  mass 
action  that  the  solubility  of  an  electrolyte  must  be  increased 
by  addition  of  another  electrolyte  not  having  a  common  ion, 
and  developed  an  expression  for  the  increase,  assuming  that 
the  two  electrolytes  were  equally  dissociated.  He  also 
examined  the  effect  of  ternary  electrolytes  upon  the  solubility 
of  binary  ones  having  a  common  ion.  Thus  by  calculating 
the  value  of  x,  the  concentration  of  the  common  ion  due  to 
the  added  electrolyte,  from  the  experimentally  determined 
solubility  of  the  binary  salt,  he  was  able  to  find  numbers 
representing  the  degree  of  dissociation  of  the  ternary  electro- 
lyte assuming  that  it  dissociated  according  to  the  scheme 

MA2^M"  +  2  A' 

Later,  Noyes  (ML  phys.  Chem.}  9,  626  (1892))  showed 


32  COMPLEX   IONS 

how  to  calculate  the  depression  in  the  case  of  two  ternary 
electrolytes,  assuming  that  dissociation  occurred  according 
to  the  same  scheme,  and  in  order  to  test  the  accuracy  of  his 
expression  he  measured  the  solubility  of  lead  chloride  in 
solutions  of  magnesium,  calcium,  zinc,  and  manganese 
chlorides.  Fair  agreement  was  found  between  the  observed 
and  calculated  values  when  the  concentration  of  the  added 
salt  was  not  greater  than  0*1  K  Above  this  concentration 
the  solubilities  found  were  higher  than  the  calculated  values. 
It  is  now  known  that  the  dissociation  of  a  ternary 
electrolyte  occurs  in  two  stages  according  to  the  scheme 

MA2^MA-  +  A' 

MA-^M-  +  A' 

This   does  not  affect   the  accuracy  of  JSToyes'  calculations, 
however,  for  on  multiplying  together  the  two  constants 
_  [MA-][A]  [MJ[A] 

kl  ~      [MA2]     '  *2  ~     [MA-] 

we  obtain  kx  7c2  =  K  =     r*i\  r 

so  that  the  product  [M'^JfA']2  is  constant  as  assumed  in  the 
calculation. 

Although  there  was  no  doubt  that  in  solutions  of  con- 
centration not  greater  than  0*1  N.  the  solubility  depression 
follows  the  path  indicated  by  the  theory  of  electrolytic  dis- 
sociation and  the  law  of  mass  action,  the  agreement  thus 
far  obtained  between  theory  and  experiment  was  not  all  that 
could  be  desired.  Two  possible  causes  were  suggested  for 
the  divergencies,  namely,  (1)  untruthfulness  of  the  law  of 
mass  action,  and  (2)  inaccuracy  in  the  (approximately 
determined)  degrees  of  dissociation  for  the  slightly  soluble 
salt  in  the  mixed  solution.  In  order  to  find  out  to  which  of 
these  causes  the  unsatisfactory  character  of  the  agreement 
was  due,  Noyes  and  Abbott  (Zeit.  phys.  Chem.,  16,  125 
(1895))  devised  a  method  of  calculating  without  approxima- 
tion from  solubility  experiments  the  value  of  the  degree  of 
dissociation  of  a  salt  in  solution  in  water.     If  the  values 


THE   SOLUBILITY   METHOD 


33 


obtained  in  this  way  agree  with  those  obtained  from  con- 
ductivity measurements,  it  follows  that  the  discrepancies 
observed  in  previous  experiments  must  have  been  due  to 
inaccuracy  in  the  approximate  calculation  of  the  values  of 
71,  and  that  the  salts  in  solution  do  strictly  obey  the  law 
of  mass  action. 

The  method  is  as  follows :   Let  s  and  s'  be  the  solubilities 
of  two  salts  in  pure  water  and  rj  and  1/  those  when  both 
salts  are  present  in  excess.     Let  7,  y,  ylf  and  y\   be  the 
corresponding  degrees  of  dissociation.     Then,  since  the  con- 
centration of  the  undissociated  molecules  of   each   salt  is 
constant  in  all  saturated  solutions,  we  have 
s(l-y)  =  r,(l  -  yi) 
•(1  -  /)  =  „'(1  -  ytO 
Further,  since  the  solubility  products  are  also  constant, 

(sy)2  =  1171(7171  +  117/) 
(s'7')2  =  r{yi(r\yi   +  ^71) 

These  four  equations  contain  only  four  unknown  quan- 
tities— the  degrees  of  dissociation.  These  can  therefore  be 
calculated  from  the  experimental  values  for  the  solubilities, 
and  they  include  the  values  for  solutions  of  the  two 
salts  in  pure  water. 

Experiments  were  conducted  by  Noyes  and  Abbott  with 
the  three  sparingly  soluble  salts,  TlCl,  TISCN,  and  TlBr03. 
The  solubility  of  each  salt  was  determined  in  water,  and  then 
the  solubilities  were  measured  in  the  three  possible  solutions 
saturated  with  respect  to  a  pair  of  the  salts.  The  con- 
ductivity of  each  salt  was  measured  in  its  saturated  solution 
in  water,  and  the  dissociation  degrees  were  calculated.  The 
following  table  shows  the  values  found : — 


Salt. 

Mean  percentage  dissocia-        Dissociation  from 
tion  from  solubility.                conductivity. 

TlCl 

TISCN 

TIBrO, 

86-5  ±  0-3 
86-6  ±  0-3 
90-2  ±  0-4 

86-6  ±  0-1 
85-6  ±0-1 
890  ±  0-1 

34  COMPLEX  IONS 

Thus  we  have  strong  reason  to  believe  that  the  law  of 
mass  action  is  obeyed  by  salts  in  dilute  solution,  and  that 
the  values  of  y  obtained  by  conductivity  measurements  are 
also  correct. 

Good  agreement  should  therefore  be  obtained  between 
observed  and  calculated  results  by  using  equation  (2),  and 
as  we  have  already  seen,  this  is  the  case. 

These  equations  only  hold  good  for  dilute  solutions  in 
which  ionisation  occurs  normally,  that  is,  when  no  complex 
ions  are  formed.  Any  departure  from  the  value  calculated 
by  the  above  methods  indicates  that  a  disturbance  of  the 
simple  conditions  assumed  in  developing  them  has  occurred. 
The  only  known  cause  of  an  increase  of  the  solubility  of  a 
salt  above  the  theoretical  value  as  calculated  is  the  formation 
of  complex  ions.  Kendall  (Proc.  Boy.  Soc,  A,  85,  200 
(1911))  showed  that  in  the  case  of  certain  acids  the  solu- 
bilities in  mixed  solutions  show  considerable  divergences 
from  the  theoretical  values,  but  in  every  case  this  can  be 
accounted  for  by  the  change  in  the  solubility  of  the  undis- 
sociated  compounds  caused  by  the  solvent  effect  of  the  acids 
upon  one  another.  In  dilute  solutions  such  divergences  do 
not  amount  to  more  than  a  few  per  cent,  of  the  solubility. 

An  example  of  the  identification  of  a  stable  complex  ion 
from  a  study  of  the  solubility  of  a  very  sparingly  soluble 
salt  in  a  solution  of  another  electrolyte  has  already  been 
given  in  Chapter  II,  where  we  saw  that  one  gram  molecule 
of  potassium  cyanide  in  solution  dissolves  exactly  (within 
the  limits  of  analytical  error)  one  molecule  of  silver  cyanide, 
yielding  a  solution  containing  potassium  ions,  but  practically 
no  silver  ions.  Hence  a  complex  ion  must  have  been  formed 
whose  composition  is  represented  by  the  formula  Ag(CN)2'. 
If  we  knew  the  concentrations  [Ag*]  and  [CN']  we  could 
calculate  the  value  of  the  dissociation  constant 

_  [Ag  1CNT 
*-[Ag(CNV] 

This  has  heen  done  by  Bodlander  and  Eherlein  (Zeit.  anorg. 


THE   SOLUBILITY   METHOD  35 

Chem.,  39,  197  (1904))  by  methods  which  will  be  discussed 
in  succeeding  chapters. 

Similarly,  four  gram  molecules  of  potassium  cyanide 
would  dissolve  one  gram  molecule  of  ferrous  cyanide,  yield- 
ing potassium  ferrocyanide,  K4Fe(CN)6,  in  which  no  ferrous 
ions  or  cyanogen  ions  are  recognisable,  but  only  potassium 
ions  and  the  complex  ion  Fe(CN)6"". 

In  the  cases  of  these  exceptionally  stable  complexes  one 
or  more  of  the  reacting  ions  disappears  completely  so  far  as 
analytical  methods — including  solubility  determinations — 
are  concerned,  and  can  only  be  identified  by  physical  means 
which  will  be  described  in  the  next  chapter. 

We  can  sometimes  gain  a  qualitative  knowledge  of  the 
concentration  of  an  ion  present  only  in  minimal  amount  by 
finding  a  reagent  with  which  it  forms  a  compound  so 
insoluble  that  even  with  the  small  quantity  of  the  ion 
present  we  can  cause  the  solubility  product  for  the  insoluble 
compound  to  be  exceeded.  Thus  by  adding  excess  of 
potassium  chloride  to  an  ammoniacal  solution  containing 
silver  we  can  cause  some  of  the  silver  to  be  precipitated  as 
chloride.  On  adding  more  ammonia  the  precipitate  is  re- 
dissolved.  Potassium  chloride  cannot  precipitate  a  visible 
amount  of  silver  chloride  from  its  solution  in  potassium 
cyanide,  but  addition  of  an  alkaline  sulphide  causes  the 
much  more  insoluble  silver  sulphide  to  separate. 

Thus  we  may  say  qualitatively  that  the  ion  Ag(CN)2'  is 
more  stable  than  the  ion  Ag(NH3)2*  (the  ion  formed  when 
silver  salts  dissolve  in  ammonia),  but  that  the  former  ion 
also  yields  minute  quantities  of  silver  ions. 

In  the  case  of  very  stable  ions  this  is  all  the  information 
the  solubility  method  can  give  us. 

When  the  complex  is  less  stable,  however,  a  more  com- 
plete knowledge  of  its  properties  can  be  arrived  at  by  means 
of  solubility  measurements  alone,  and  we  shall  now  describe 
the  methods  by  which  such  information  may  be  gained. 

A  general  method  for  the  determination  of  the  constitu- 
tion of  a  complex  ion  from  solubility  measurements  was 


36  COMPLEX   IONS 

first  given  by  Sherill  (Zeit.  phys.  Chem,,  43,  705  (1903))  and 
applied  by  him  to  the  case  of  the  mercury  halides.  In  this 
case  the  following  general  relations  hold,  where  X  represents 
an  atom  of  the  halide  : — 

1.  Hg2X2^HgX2  +  Hg 
or  in  terms  of  the  reacting  ions 

Hg2"^Hg"  +  Hg 

This  equilibrium  was  observed  by  Eichards  (Zeit.  phys. 
Chem.,  24,  39  (1897)),  and  investigated  by  Abel  (Zeit.  anorg. 
Chem.,  26,  361  (1901)),  who  showed  that  the  mercurous  ion 
has  the  formula  Hg2",  and  found  the  value  of  the  constant 

K-wr120 

the  concentration  of  the  metallic  mercury  being  constant. 

2.  mHgX2  +  nX'  ^  (HgX2)„(X% 

_  [(HgX^X'^] 
*l  -  [HgX2]»[X']» 

3.  HgX2^Hg"  +  2X' 

_  [Hg"][X'P 
K>~     [HgX2] 

4.  Hg2X2^Hg2-  +  2X' 

_  [Hga-f  XT 
*8-     [Hg2X2] 

If  the  mercurous  salt  is  present  in  excess  its  concentration 
in  the  solution  will  be  constant,  and  thus  from  (1)  the 
concentration  of  undissociated  mercuric  halide  is  also 
constant.  Thus  the  undissociated  mercurous  halide  behaves 
like  a  less  soluble  modification  of  the  mercuric  halide  which 
is  an  equilibrium  with  it. 

From  (2)  we  obtain 

[(HgX2UX')„]  =  Ki[HgX2]„  =  K<  9 

Since  the  amount  of  free  mercuric  halide  .  present  in  an 
alkali    halide    solution    (in   which    the   experiments    were 


THE   SOLUBILITY   METHOD  37 

conducted)  is  very  small,  we  may  put  the  total  content 
of  mercuric  halide  in  the  solution  equal  to  the  mercuric 
mercury  content  of  the  complex.  Compared  with  the 
total  amount  of  mercury  in  the  solution  the  solubility  of 
the  mercurous  halide  is  also  negligible,  so  that  analytically 
the  amount  of  mercury  present  as  complex  is  given  by  the 
solubility  of  the  mercurous  salt.  That  no  appreciable  amount 
of  mercurous  complex  ion  is  formed  is  shown  by  the  fact 
that  (analytically)  the  solution  contains  only  mercuric  halide. 

Let  a  be  the  initial  concentration  of  alkali  halide,  c  the 
concentration  of  mercuric  halide  present  as  complex.  In  the 
present  case  we  may  put  c  equal  to  the  concentration  of 
mercurous  salt  dissolved. 

We  thus  obtain  the  equation 


K*  = 


(a c) 


in  which  m  and  n  are  unknown  integers  and  K  is  a  constant 
of  unknown  value.  For  practical  purposes  we  may  assume 
complete  dissociation  of  the  alkali  halide  and  of  the  complex 
salt. 

We  now  proceed  to  find  by  trial  values  of  m  and  n  (whole 
numbers)  which  cause  K4  in  the  above  expression  to  remain 
constant  while  the  concentration  of  the  alkali  halide  (which 
determines  the  apparent  solubility  of  the  mercurous  halide) 
is  altered. 

This  method  is  based  upon  measurements  of  the  solubility 
of  the  salt  forming  the  "  neutral  part "  in  solutions  of  that 
providing  the  separate  ion. 

Another  method  of  attacking  the  problem  which  is  useful 
in  cases  where  the  neutral  part  is  itself  freely  soluble  is  based 
upon  measurements  of  the  solubility  of  a  sparingly  soluble 
salt  yielding  the  separate  ion  as  a  product  of  its  dissociation. 
This  gives  us  the  concentration  of  the  separate  ion  in 
any  solution. 


38  COMPLEX   IONS 

We  may  consider  the  case  of  a  salt  BA  which  dissociates 
according  to  the  scheme 

BA^B+ A' 
the  extent   of  the   dissociation    being  determined   by   the 
equation 

K  _  [Bj[A'] 
~    [BAT 
In  saturated  solution  the  product  [B*][A']  is  constant.     We 
may  call  this  L  and  the  concentration  of  the  undissociated 
part   A.     Then  in  any   solution  the   concentration   of  the 
separate  ion  A  is  given  by 

where  ?j  is  the  solubility  of  the  salt  BA  in  the  solution. 
[A']  here  includes  the  ions  provided  by  the  salt  BA  itself. 

L  and  A  may  be  determined  by  measuring  the  conductivity 
of  a  saturated  solution  of  the  salt  BA  in  water,  or,  if  the 
solubility  be  very  small,  by  indirect  means. 

A  third  method  of  attack  by  means  of  solubility  consists, 
theoretically,  in  determining  the  solubility  of  the  salt 
providing  the  "  free  ion "  in  solutions  of  that  forming  the 
neutral  part.  Up  to  the  present  this  has  not  been  employed, 
as  it  has  generally  been  found  convenient  to  use  alkali  salts 
for  providing  the  free  ion,  and  the  solubility  of  these  is  usually 
too  large  to  admit  of  mathematical  treatment  according  to 
the  simple  law  of  mass  action. 


CHAPTER  VI 

THE  ELECTRICAL  POTENTIAL  METHOD 

This  method  consists  in  deducing  the  concentration  of  an 
ion  in  solution  from  measurements  of  the  potential  of  an 
electrode  which  dips  into  it. 

If  a  strip  of  a  metal  dips  into  a  solution  containing  ions 
of  the  same  metal  a  difference  of  potential  is,  in  general, 
produced  at  the  boundary  between  metal  and  liquid,  so  that 
the  metal  strip  becomes  either  positively  or  negatively 
charged  with  respect  to  the  solution.  If  the  ion  has  the 
valency  n,  and  we  denote  the  charge  per  gram  equivalent 
(96,540  coulombs)  by  F,  and  the  difference  in  potential  by 
E,  the  electrical  work  done  by  the  system  when  one  gram 
ion  passes  from  the  electrode  is  nFE  joules,  the  sign  depend- 
ing upon  the  sign  of  the  E.M.F.  At  the  concentration  of 
the  solution  let  this  gram  ion  occupy  a  volume  v  under 
the  osmotic  pressure  p. 

We  may  next  allow  this  gram  ion  to  expand  to  a  volume 
v  -f  dv  under  the  corresponding  pressure  p  —  dp.  The 
system  thus  yields  the  further  quantity  of  work  pdv,  neglect- 
ing terms  of  the  second  order.  Let  the  E.M.F.  now  be 
E  +  d& 

Finally,  let  our  gram  ion  be  re-deposited  on  the  elec- 
trode, requiring  the  expenditure  of  the  quantity  of  work 
nF(E  +  dE),  and  leaving  the  system  in  its  initial  state. 

Adding  together  the  quantities  of  work  yielded  by  the 
system  (positive)  and  performed  upon  it  (negative)  we 
obtain 

tiFE  +  pdv  -  7iF(E  +  dE)  =  0 
whence  ?iFdE  =  pdv 

39 


40  COMPLEX   IONS 

From  the  gas  laws, 


and 

pdv  = 

v  = 

—  vdp 
ET 

Hence 

»F 

.dE  = 

-ET 

from  which 

we 

obtain 

-dp 
p 


n¥E  =  -  ET  loge  p  +  a  constant 

We  may  put  this  constant  equal  to  ET  log  P,  where  P  is  a 
constant  having  the  dimensions  of  pressure.  It  is  then 
evident  that  if  p  =  P,  E  =  0,  and  the  system  is  in  equili- 
brium. P  is  therefore  called  the  electrolytic  solution  pressure 
for  the  metal  under  consideration.     We  thus  obtain 

ET  ,  ,ET.       ^ 

E=-^logei>+^logeP 

-,      ET  ,       P 

or  E  =  -^  log  - 

nF     °e  p 

F  being  measured  in  coulombs  and  E  in  joules,  E  is  given 
in  volts  by  this  expression. 

The  E.M.F.  existing  between  a  single  electrode  and  a 
solution  surrounding  it  is  called  an  electrode  potential. 

The  osmotic  pressure,  p,  is  proportional  to  the  concentra- 
tion of  the  ions,  which  we  may  call  c.  Thus  we  get  the 
equation 

V=e0--flogec 

If  c  be  measured  in  gram  ions  per  litre,  e0  is  the  E.M.F. 
when  the  solution  contains  one  gram  ion  per  litre.  This 
E.M.F.  is  called  the  electrolytic  potential  of  the  ion  concerned. 

This  quantity  has  been  determined  for  most  of  the 
elements.  As  is  readily  to  be  seen  from  the  form  of  the 
expression,  e0  can  be  calculated  if  we  measure  E  for  a  solution 
in  which  the  concentration  of  the  ions  is  known. 

Taking   E  =  8-315  joules,  F  =  96,540  coulombs,  fixing 


THE  ELECTEICAL  POTENTIAL  METHOD      41 

T  at  25°  C,  i.e.  298°  abs.,  and  transforming  the  logarithm  to 
the  base  10,  we  obtain 

v  0-059 . 

Thus  we  see  that  at  25°  0.  the  potential  of  a  monovalent 
metal  changes  by  0*059  volt  for  every  change  of  tenfold  in 
the  ionic  concentration  of  the  solution,  and  the  potential  of 
a  divalent  metal  changes  by  0*0295  volt  under  the  same 
conditions. 

Proportionate  values  for  the  change  of  E.M.F.  may  be 
calculated  for  other  temperatures. 

In  the  above  calculation  we  have  assumed  that  work  is 
done  by  the  system  when  the  electrode  dissolves,  and  hence 
that  E  increases  as  the  solution  becomes  more  dilute.  This 
is  true  if  we  consider  the  ion  to  be  a  kation,  and  the  potential 
that  of  the  solution  with  respect  to  the  electrode.  Another 
system  is  in  use  in  which  the  sign  of  the  E.M.F.  is  reversed, 
and  the  potential  is  reckoned  positive  when  the  electrode  is 
positive  to  the  solution.     In  this  case 

E  =  e°  +  nF  l0ge  C 
In  each  case  the  sign  must  be  reversed  if  the  ion  is  an 
anion  instead  of  a  kation. 

In  a  cell  of  the  general  type 

Metal  I|Electrolyte  I|Electrolyte  II|Metal  II 

in  addition  to  the  potential  differences  at  the  two  boundaries 
between  electrode  and  electrolyte  there  is  generally  a  differ- 
ence of  potential  between  the  two  electrolytes,  and  in  earlier 
investigations  much  difficulty  was  occasioned  by  the  fact 
that  in  many  cases  this  potential  could  not  be  determined. 

The  difference  of  potential  across  the  liquid  boundary 
between  two  electrolytes  is  entirely  due  to  diffusion,  since 
no  chemical  reaction  is  involved  in  the  passage  of  the 
current.  If  we  imagine  a  solution  of  hydrochloric  acid  in 
contact  with  water,  both  kinds  of  ion  (H*  and  CI')  will 
diffuse  from   the   acid    solution   into   the   water.     As   the 


42  COMPLEX   IONS' 

hydrogen  ion  tends  to  move  faster  than  the  chlorine  ion, 
hydrogen  ions  will  accumulate  in  the  water  in  excess  of  the 
chlorine  ions,  giving  the  water  a  positive  charge  with  respect 
to  the  acid.  This  will  continue  until  the  potential  reaches 
a  certain  value,  high  enough  to  check  further  separation  of 
the  two  ions,  the  system  thus  reaching  a  state  of  equilibrium. 
It  is  easy  to  calculate  the  difference  of  potential  which 
arises  at  the  boundary  of  two  solutions  of  the  same  binary 
electrolyte  of  different  concentrations.  Let  the  osmotic 
pressure  due  to  each  ion  be  pi  and  p2  m  the  stronger  and 
weaker  solutions  respectively,  and  let  the  transport  number 
for  the  anion  be  x.  If  one  faraday  now  passes  through  the 
solution  from  the  stronger  to  the  weaker  portion,  the  osmotic 
work  done  upon  the  system  is 

x .  KT  loge P~-a-  a)KT  loge g  =  (2x  -  1)ET  loge|i 

Since  the  tendency  of  the  ions  to  separate  by  diffusion  is 
balanced  by  the  E.M.F.  produced,  this  expression  is  equal  to 
the  electrical  work  FE,  and  we  find 

If  we  call  the  ionic  mobilities  for  the  anion  and  the  kation 
11a  and  uk  respectively 

r£     =     _ 

and  hence  E=*^K-^loge^ 

If  u±  =  uK  the  E.M.F.  is  nil ;  and  the  magnitude  and  sign 
of  the  potential  depends  upon  the  relative  values  of  the  ionic 
mobilities. 

The  above  case — that  of  two  solutions  of  the  same  binary 
electrolyte — is  the  simplest  one.  Equations  applicable  to 
more  complex  systems  have  been  worked  out  by  Planck 
(Wied.  Annalen,  40, 561  (1890)),  K.  K.  Johnson  (Annalen  der 
Physik,  14,  995  (1904)),  Henderson  (Zeit.phys.  Chem.,  59, 118 
(1906);  63,  325  (1908)),  and  Cumming  (Trans.  Farad.  Soc, 


THE   ELECTKICAL   POTENTIAL   METHOD       43 


vol.  8,  1912).  The  equation  of  Planck  and  its  extension  by- 
Johnson  are  excessively  complicated,  and  in  the  case  of 
polyvalent  ions  the  practical  solutions  contain  an  element  of 
uncertainty  (Bjerrum,  Zeit.  phys.  Chem.,  53,  428  (1905)). 
Henderson's  equation,  however,  is  simpler,  besides  being 
based  on  premises  which  probably  approximate  more  closely 
to  practical  conditions.  It  has  been  further  simplified  by 
Cumming  for  the  case  where  the  anion  and  kation  of  each 
salt  has  the  same  valency.  These  equations  can  be  compara- 
tively easily  applied  in  practice,  and  give  results  which  agree 
well  with  the  values  observed  in  control  experiments,  where 
the  sum  of  the  electrode  potentials  is  known. 

Several  experimenters  have  endeavoured  to  find  means  to 
eliminate  practically  the  diffusion  potential  in  two-liquid 
cells.  Tower  (Zeit.  phys.  Chem.,  20,  198  (1896))  studied  the 
effect  of  interposing  between  the  electrolytes  a  strong  solu- 
tion of  a  salt  yielding  ions  whose  mobilities  were  nearly 
equal  to  one  another,  such  as  potassium  chloride.  As  an 
example  we  may  quote  the  values  obtained  by  him  for 
the  cell 

Mn02,  0-1  N.  HNO8|KCl|0-05  N.  HN03,  Mn02 
which  are  contained  in  the  following  table.     The  calculated 
values  for  the  diffusion  E.M.F.'s  are  calculated  by  means  of 
Planck's  formula.      In  each  case  the  acid  solutions   were 
0'005  K  with  respect  to  Mn(JTO3)2.   This  small  concentration 


was  neglected  in  calculating  the  diffusion  P.D. 

Calculated  P.D.  at  boundary 

»KC1 

(litres). 

between  KC1  and 

Total  P.D.  due  to 
diffusion  (calcu- 
lated). 

Total  P.D.  of 
cell,  calculated. 

P.D. 

observed. 

0-1  N.  HN03 

0-05  N.  HNO3 

1 

-0-0125 

0-0090 

-00035 

0-0311 

0033 

2 

-0-0169 

0-0120 

-0-0049 

00297 

0-031 

4 

-0-0222 

0-0169 

-0-0053 

0-0293 

0030 

8 

-00282 

0-0219 

-0-0063 

0-0283 

0028 

16 

-00352 

0-0280 

-0-0072 

0-0274 

0027 

32 

-0-0430 

0-0350 

-0-0080 

00266 

0-025 

64 

-00516 

0-0429 

-0-0087 

0-0258 

0024 

128 

-00607 

00515 

-0-0092 

• 

00254 

0023 

44  COMPLEX  IONS 

The  total  E.M.F.  of  a  similar  cell  containing  no  potassium 
chloride  and  with  the  acid  solutions  in  contact  with  one 
another  was  0*023  volt,  the  calculated  value  being  0'0225 
volt.  (This  value  is  obtained  by  means  of  the  ordinary 
formula  for  oxydation-reduction  cells,  which  in  this  case 
takes  the  form 

*      2F    fc*[H-]!4 

bearing  in  mind  that  the  concentration  of  Mn"  ions  may  be 
taken  as  equal  in  the  two  solutions.) 

The  total  calculated  electrode  E.M.F.  is  0'035  volt. 

From  these  and  similar  results  Tower  concluded  that 
the  interposition  of  strong  solutions  of  potassium  chloride 
between  different  electrolytes  has  a  certain  tendency  to 
diminish  the  diffusion  potential,  which  disappears,  however, 
as  the  solution  is  made  more  dilute. 

From  this  time  onwards  the  method  was  generally  used, 
but  it  possessed  the  disadvantage  that  in  cases  where  the 
diffusion  potential  could  not  be  calculated  it  was  impossible 
to  fix  definite  limits  to  the  error  caused  by  the  small 
remaining  P.D. 

The  problem  was  further  studied  by  Bjerrum  (loc.  cit), 
who  extrapolated  to  find  the  potential  due  to  the  action  at 
the  electrodes  alone,  from  measurements  with  saturated  and 
half-saturated  solutions  of  potassium  chloride,  on  the  assump- 
tion that  the  unremoved  potential  due  to  diffusion  in  the 
former  case  was  half  that  in  the  latter.  Very  satisfactory 
agreement  was  found  between  the  extrapolated  values  and 
those  obtained  by  calculating  the  diffusion  potentials  without 
the  insertion  of  a  middle  electrolyte  and  subtracting  these 
from  the  values  obtained  by  measurement  under  the  same 
conditions.  Bjerrum  concluded  that  the  error  in  the  extra- 
polated values  could  only  at  the  most  be  of  the  same  order  of 
magnitude  as  the  difference  between  the  potentials  found 
experimentally,  using  saturated  and  half-saturated  solutions 
of  potassium  chloride  respectively. 


THE  ELECTRICAL  POTENTIAL  METHOD      45 

A  further  great  improvement  was  introduced  by  Cum- 
ming  {Trans.  Faraday  Soc,  2,  213  (1907)),  who  found  that  in 
cells  of  the  types 

Hg|Hg2Cl2,  0-1  N.  HC1|1*0  N.  HC1,  Hg2Cl2|Hg 
and 

Hg|Hg2Cl2,  01  N.  LiCl|l*0  N.  LiCl,  Hg2Cl2|Hg 

the  diffusion  E.M.F.  was  almost  entirely  removed  by  inter- 
posing a  saturated  solution  of  ammonium  nitrate  between  the 
two  electrolytes. 

The  cells  were  chosen  so  as  to  have  large  diffusion 
potentials,  the  kation  moving  much  faster  than  the  anion  in 
the  first  case  and  much  more  slowly  in  the  second.  For  the 
first  cell  the  calculated  electrode  E.M.F  is  0*0563  volt.  The 
mean  experimental  value  for  the  E.M.F.  of  the  cell  was 
found  to  be  0*0950  volt.  When  saturated  ammonium  nitrate 
was  interposed  between  the  two  hydrochloric  acid  solutions 
the  E.M.F.  was  0*0565  volt. 

In  the  second  case,  the  observed  E.M.F.  of  the  cell  was 
0*0361  volt,  and  the  diffusion  potential  calculated  from  con- 
ductivity data  was  0*0169  volt  acting  in  the  opposite  direc- 
tion to  the  electrode  E.M.F.  Adding  together  these  values 
we  obtain  for  the  electrode  E.M.F.  the  value  0*0530  volt; 
or  calculating  the  electrode  E.M.F.  from  Nernst's  formula  we 
find  e  =  0*0522  volt.  When  a  10  N.  solution  of  ammonium 
nitrate  was  interposed  between  the  electrolytes  the  E.M.F. 
of  the  cell  was  found  to  be  0*0543  volt. 

It  is  therefore  probable  that  in  general  the  diffusion 
potential  between  two  electrolytes  is  nearly  all  removed  by 
interposing  a  concentrated  solution  of  ammonium  nitrate 
between  them.  Since  its  introduction,  this  method  of 
removing  diffusion  potentials  has  been  extensively  used. 

The  electrical  potential  method  has  been  one  of  the  most 
fruitful  ones  in  the  investigation  of  complex-formation.  A 
general  preliminary  study  of  the  behaviour  of  a  number  of 
salts   from   this   point   of  view   was   made  by   Abegg  and 


46  COMPLEX   IONS 

Labendzinski  (Zeit.  fur  Elektrochemie,  10  (1904)),  who 
measured  the  E.M.F.'s  of  cells  of  the  type 

Metal|Salt  of  metal|l*0  N.  calomel  electrode 

using  the  nitrate,  chloride,  sulphate,  and  acetate  of  various 
metals.  The  potentials  observed  showed  that  at  a  given 
concentration  the  amounts  of  metal  ions  present  varied 
enormously  according  to  the  character  of  the  anion,  and  for  the 
following  series  of  anions  continuously  decreased  :  N03',  CI', 
S04",  C2H302'.  Since  conductivity  measurements  show  that 
salts  of  all  these  anions  are  largely  electrolytically  dissociated, 
it  follows  that  complex- formation  must  have  occurred,  causing 
the  concentration  of  free  metal  ions  to  fall  to  very  small  values. 
In  order  to  find  the  constitution  of  a  complex  ion,  it  is 
not  necessary  to  know  the  absolute  concentrations  of  the 
components  in  the  system.  All  we  need  is  to  find  their  rate 
of  change  with  respect  to  one  another,  so  as  to  be  able  to 
obtain  the  indices  in  an  equation  of  the  type 

,.      [Mf[AT 

in  which  M*  represents  a  positively  charged  ion,  A'  a 
negatively  charged  one,  and  the  complex  ion  MgAr  has  q  —  r 
positive  charges  (or  r  —  q  negative  ones).  A  method  of  doing 
this  was  first  given  by  Bodlander  (Festschrift  zu  Dedekind, 
Braunschweig,  1901),  and  we  shall  now  describe  this. 

Applying  the  above  equation  to  two  solutions  of  different 
concentrations,  we  obtain 

[Mf  _  [M,Ar]i  [Ay 
[M-],«      [M,AJ2  [A!y 

We  now  proceed  to  make  [A']i  =  [A']2.  This  can  be 
achieved  in  practice  by  working  with  small  concentrations 
of  the  metal  M  (and  therefore  of  M*  and  M3Ar)  in  presence 
of  a  large  excess  of  another  salt  having  A'  as  its  anion. 
Under  these  conditions 

[M']i«  =  QMrfc 

[M-y      [M,AJ2 


THE   ELECTEICAL  POTENTIAL   METHOD      47 

If  e   be  the^  electrode  E.M.F.  of  the  concentration  cell 
M'Solution  I|Solution  II|M 

.  ET,      [M-Jx 

we  nave  e  =  — ^log^*-  i 

nF    to  [M-]2 

=  ^iog(BM)i 

»*     &V[M,Ar]/ 

,  ET,      [MAr]x 

whence  q  =  — rrlogfW1- 


nFe    °  [M  A 


In  cases  where  the  complex  ion  is  known  to  be  stable,  as, 
for  example,  in  solutions  of  silver  chloride  in  ammonia  where 
the  solubility  is  almost  entirely  due  to  complex  formation, 
the  complex-concentration  [MgAr]  (M  in  this  case  stands  for 
the  metal  while  A  represents  an  ammonia  molecule)  may  be 
written  equal  to  the  total  concentration  of  the  metal,  without 
sensible  error.      We  can  thus  solve  the  above  equation  for  q. 

Similarly  we  may  find  r  by  making  the  concentrations  of 
the  complex  ion  in  the  two  solutions  equal  to  one  another. 
We  then  obtain  the  equation 

[M-y  _  [Ay 

RTi     [M']i 
Now  ^-logLX 

mF    ol[A']/ 
r  e 

Hence  q =  ET       \A'\2 

rf^CATx 
from  which  we  find  the  value  of  r.    We  thus  obtain  the 
composition  of  the  complex  ion. 

This  theorem  has  been  extended  ( Jaques,  Trans.  Faraday 
Soc,  5,  225  (1910))  to  the  case  in  which  the  concentrations 
of  the  complex  ion  in  the  two  solutions  are  not  equal.  In 
this  case,  as  before 

[M-]ig_[M,Ar],  [AV 
[M-]a«     [M,Ar]2'  [AV 


48  COMPLEX  IONS 

We  now  have  e  =  -rJog  m  J1 
wF    6[M-]2 

_^T       /[MgAr]iy/[A12\j 
~  rf10H[MgAr]2^  V{AV 

*  M10&[MgAr]2  +  ?10-[A']J 

r  RT,     [A']2             1  RT,      [M^AJi 
Thus  -  — =5 log fttT3*  ^ ^log 


?  »F  V&[A']X  2   nFw°[MgAr]a 

whence,  putting   [M9Ar]i  and   [MgAr]2  equal  to  Cx  and  C5 
respectively,  we  obtain 


r  = 


RT,     C2 


wF1°b[A']1 


This  equation  can  in  general  be  solved,  remembering  that  q 
and  r  are  necessarily  integers  (cf.  Appendix  2). 


CHAPTER   VI I 

SOME  EXAMPLES 

As  an  example  of  the  application  of  the  methods  developed 
in  the  two  preceding  chapters,  we  may  consider  the  case  of 
the  mercuric  halide  complexes. 

As  early  as  1842  Miahle  (Ann.  Ghim.  Phys.)  observed 
that  mercuric  chloride  was  much  more  soluble  in  solutions 
of  chlorides  than  in  water.  According  to  our  present  theory 
this  is  a  sure  indication  of  the  formation  of  a  complex  ion. 
Under  normal  circumstances  the  solubility  would  be  de- 
pressed by  the  presence  of  chlorine  ions,  and  any  excess  of 
solubility  over  that  calculated  from  the  law  of  mass  action 
must  be  caused  by  a  portion  of  the  salt  having  been  removed 
from  direct  equilibrium  with  the  chlorine  and  mercury  ions, 
as  explained  in  Chapter  V.  The  ionisation  of  mercuric 
chloride  is  actually  very  slight,  so  that  the  calculated 
solubility  in  a  chloride  solution  would  be  very  little 
different  from  the  value  in  water.  The  equation  for  equili- 
brium, 

[Hg"][ClT 
LHgClJ     ~* 

must  hold  good,  however,  and  the  excess  of  mercuric  chloride 
must,  therefore,  be  regarded  as  having  ceased  to  function  as 
a  component  in  this  system. 

Le  Blanc  and  Noyes  (Zeit.  phys.  Chem.,  6,  401  (1890)) 
studied  the  problem  of  determining  the  constitution  of  such 
solutions  by  means  of  cryoscopic  measurements.  These 
afford  still  another  method  of  investigating  the  formation  of 
complex  ions.     Since  the  depression  of  the  freezing  point  of 

49  E 


50 


COMPLEX   IONS 


a  solvent  is  proportional  to  the  number  of  molecules  per  unit 
volume  (for  dilute  solutions)  that  it  contains,  we  can  find 
out  whether  two  substances  form  a  compound  in  solution  by- 
measuring  the  freezing  point  of  the  mixed  solution,  and,  if 
the  combination  is  practically  complete,  in  what  proportions 
the  substances  combine  with  one  another. 

Le  Blanc  and  Noyes  determined  the  freezing  points  of 
solutions  of  hydrochloric  acid  in  which  various  amounts  of 
mercuric  chloride  were  dissolved.  The  following  table  shows 
the  results  obtained  by  them  for  1*0  N.  hydrochloric  acid  : — 


Cone,  of  HgCl2 
mols.  per  litre. 

Freezing  point. 

Difference. 

0 

-3-965 

1 

-3-785 

0-180 

1 

-3-560 

0225 

i 

-3-435 

0125 

i 

-3-350 

0085 

-3-380 

-0030 

-3-395 

-0015 

i 

-3-425 

-0-030 

The  fact  that  on  adding  small  quantities  of  mercuric 
chloride  to  the  solution  the  freezing  point  rises,  shows 
definitely  that  a  diminution  in  the  number  of  molecules  in 
the  solution  has  occurred.  From  the  above  results  and 
those  obtained  at  other  concentrations  of  hydrochloric  acid 
it  was  found  that  the  maximum  in  the  freezing  point  occurs 
when  half  a  molecule  of  mercuric  chloride  is  present  for 
each  molecule  of  hydrochloric  acid. 

If  one  molecule  of  hydrochloric  acid  attached  itself  to 
one  molecule  of  mercuric  chloride,  and  the  reaction  were 
complete,  the  freezing  point  would  remain  unchanged.  It 
follows  that  at  least  two  molecules  of  hydrochloric  acid 
must  combine  with  a  molecule  of  mercuric  chloride,  unless 
we  suppose  that  the  rise  in  the  freezing  point  is  caused  by 
the  (monobasic)  complex  acid  having  a  very  much  smaller 
degree  of  dissociation  than  hydrochloric  acid.  Special  ex- 
periments were  made  to  settle  this  point. 


SOME  EXAMPLES  51 

From  a  knowledge  of  the  freezing  point  and  the  elec- 
trical conductivity  of  mercuric  chloride  solutions  alone  it 
was  evidently  impossible  that  the  degree  of  dissociation  of 
free  hydrochloric  acid  could  be  appreciably  affected  by  the 
very  small  concentration  of  chlorine  ions  produced  by  the 
mercuric  chloride. 

Turning  our  attention  to  the  case  where  two  molecules  of 
hydrochloric  acid  combine  with  one  of  mercuric  chloride,  we 
obtain  the  following  scheme  for  the  reaction  between  (1)  the 
dissociated  molecules  and  (2)  the  undissociated  molecules, 
assuming  that  the  ionised  hydrochloric  acid  yields  ionised 
complex  acid,  and  that  the  unionised  hydrochloric  acid  yields 
unionised  complex  acid  : — 

(1)  nTL'  +  JttCl'  4-  JwCr  +  (£»HgCl9)  =  friMgPk"  +  nil- 

(2)  i^HCl  4-  J»HC1  +  (^HgCl2)  =  |7iH2HgCl4 

We  thus  find  that,  compared  with  the  original  solution  of 

hydrochloric  acid  of  concentration  n  molecules  per  litre,  the 

complex  solution  contains  \n  molecules  per  litre  less.     For 

a  normal  solution  of  hydrochloric  acid  the  maximum  rise  in 

the  freezing   point  that   could   be   caused   by   addition  of 

mercuric  chloride  should  therefore  be  half  the   molecular 

1'89° 
depression  of  the  freezing  point  for  water,  viz.  — ^—  =  0'95°. 

The  maximum  rise  actually  found  was  0*62,  so  that  if  the 
acid  H2HgCl4  is  formed,  its  formation  must  be  incomplete. 
This  hypothesis  is  borne  out  by  the  fact  that  in  weaker 
solutions  of  hydrochloric  acid  the  rise  in  the  freezing  point 
is  proportionately  less,  as  would  follow  from  the  law  of  mass 
action. 

If  compounds  containing  more  than  two  molecules  of 
hydrochloric  acid  to  one  of  mercuric  chloride  are  formed, 
these  must  be  still  more  dissociated  into  their  constituent 
molecules,  and  a  simple  calculation  shows  that  under  these 
circumstances  the  concentration  of  free  mercuric  chloride 
would  reach  the  limit  of  its  solubility  before  the  solution 
actually  ceases  to  dissolve  the  salt. 


52 


COMPLEX   IONS 


We  are  therefore  obliged  to  conclude  that  either  (1)  the 
compound  H2HgCl4  is  formed  but  shows  a  considerable  dis- 
sociation into  HC1  and  HgCl2  (electrolytically  it  cannot  be 
much  more  dissociated  than  hydrochloric  acid),  or  (2)  that 
the  compound  HHgCl3  is  formed  and  is  much  less  electro- 
lytically dissociated  than  HC1. 

In  order  to  decide  this  point  measurements  were  made  of 
the  speed  of  catalysis  of  methyl  acetate  by  the  complex 
solution,  and  it  was  found  that  the  rate  was  practically  in- 
dependent of  the  presence  of  mercuric  chloride.  Thus  the 
complex  acid  must  be  highly  dissociated,  and  we  conclude 
that  the  compound  H2HgCl4  is  formed  and  is  a  strong  acid, 
dissociating  to  about  the  same  extent  as  hydrochloric  acid, 
and  yielding  the  complex  ion  HgCl4". 

The  same  authors  studied  solutions  of  iodine  in  potas- 
sium iodide  solutions  in  a  similar  manner,  and  found  that 
addition  of  iodine  to  potassium  iodide  caused  a  slight 
rise  in  the  freezing  point  instead  of  the  very  considerable 
lowering  that  would  be  produced  if  no  combination  had 
occurred.  Constancy  of  the  freezing  point  would  indicate 
the  formation  of  the  compound  KI3,  according  to  the  scheme 

KI  +  I2^KI3 

We  thus  obtain  additional  evidence  for  the  existence  of  this 
complex  compound,  accompanied  probably  by  small  quan- 
tities of  higher  iodides,  in  exact  agreement  with  the  results 
of  EolofT  and  of  Jakowkin,  which  were  given  in  Chapter  IV. 
Eeturning  to  the  subject  of  the  mercuric  halide  com- 
plexes, Kichards  (Zeit.  phys.  Chem.,  24,  39  (1897)),  in  the 
course  of  an  investigation  of  the  temperature  coefficient  of 
the  E.M.F.  of  the  calomel  electrode,  observed  that  the 
calomel  was  noticeably  decomposed  into  mercuric  chloride 
and  mercury  in  presence  of  other  chlorides,  and  ascribed  the 
apparent  acceleration  of  the  reaction  by  chlorides  to  a 
"  catalytic  "  effect.  Later  {Zeit.  phys.  Chem.,  40,  385  (1902)) 
Eichards  and  Archibald  studied  the  action  of  various  chloride 
solutions  upon  calomel,  and  found  that  the  system  reached 


SOME  EXAMPLES  53 

a  definite  equilibrium-point.  The  amount  of  mercuric 
chloride  in  the  solution  increased  with  increase  of  the 
chloride  concentration,  and  this  increase  was  roughly  pro- 
portional to  the  square  of  the  concentration  of  chlorine  ions 
in  the  solution.  We  may  represent  the  system  by  the 
scheme 

Hg2CWHgCl2    +    Hg 

H         H         tt 

Solid  TT^ni  Liquid 

Calomel.  -"-g<^l(2  +  x)  Mercury. 

from  which  we  see  that  of  the  three  substances  entering 
into  the  reaction,  the  concentrations  of  two  (calomel  and 
mercury)  are  fixed.  The  concentration  of  the  third  com- 
ponent is  therefore  also  fixed,  that  is,  the  concentration  of 
HgCl2-molecules  must  have  a  constant  value  if  the  solution 
is  in  contact  with  solid  calomel  and  liquid  mercury.  The 
excess  of  mercuric  chloride  must  therefore  be  present  as 
some  other  compound,  and  since  this  is  conditioned  by  the 
presence  of  chlorine  ions  it  must  be  in  the  form  of  either 
(1)  a  complex  ion  of  the  type  HgCl(2  +  %),  or  (2)  the  corre- 
sponding undissociated  double  salt.  As  already  pointed  out 
in  Chapter  V,  the  amount  of  mercury  in  an  aqueous  solution 
of  calomel,  including  the  mercuric  chloride  produced,  may 
be  neglected  in  comparison  with  the  total  content  of  a 
saturated  solution  containing  alkali  chloride,  and  we  may 
therefore  take  the  total  mercury  content  of  the  solution  as 
being  present  as  complex  ion.  This  should  be  proportional 
to  the  icth  power  of  the  chlorine  ion  concentration,  since 

[HgCl2][Cl>==£.[HgC1(2+!C)] 
x  must  therefore  be  approximately  2,  or,  in  other  words, 
the  complex  HgCV  is  formed  in  larger  quantities  than  any 
others. 

The  formation  of  complex  ions  in  solutions  of  mercuric 
cyanide,  chloride,  bromide,  and  iodide  was  exhaustively  studied 
by  Sherill  {Zeit.  phys.  Chem.,  43,  705  (1903)),  who  first 
developed  the  scheme  for  the  measurement  of  the  dissocia- 
tion  constant   of  a  complex    ion  by  means   of  solubility 


54 


COMPLEX   IONS 


measurements  given  in  Chapter  V.  Sherill  measured  the 
potential  of  the  cell 

Hg|Hg(CN)2  +  KCN|1'0N.KC1,  HgCl2|Hg 

using  various  concentrations  of  mercuric  cyanide  and 
potassium  cyanide  respectively.  No  precautions  were  taken 
to  estimate  or  eliminate  diffusion  potential.  This  would 
probably  be  small,  however,  as  the  molecular  conductivity  of 
potassium  cyanide  does  not  differ  much  from  that  of  potassium 
chloride,  so  that  the  mobility  of  the  cyanogen  ion  must  be 
nearly  the  same  as  that  of  the  chlorine  ion.  The  accom- 
panying table  shows  the  values  that  were  found : — 


No. 

Cone. 
KCN. 

Cone. 
Hg(CN)2. 

E.M.F. 

against 
N.E. 
volts. 

E.M.F. 
against 
No.  1 

VOlt8. 

E.M.F.  against 

No.  1  calculated 

from  formula 

Hg(CN)2(CN)2" 

volts. 

Cone,  of 
Hg". 

[Hg(CN)2(CN)2"] 
[Hg"][CN']4 

1 
2 
3 
4 
5 
6 

0049 

00983 

00983 

01965 

01965 

0-1965 

0-01247 
0-01247 
0-02493 
0-01247 
0  02493 
0-04985 

0-519 
0-575 
0-547 
0-616 
0-600 
0-574 

0056 
0-028 
0-097 
0-081 
0055 

0-057 
0-027 
0102 
0084 
0054 

1-3. 10-37 
1-7. 10  -39 
1-7. 10 -38 
0-7. 10  -40 
2-5. 10-40 
1-8. 10- 39 

2-8 .  10" 
2-5.10" 
2-7.10" 
2-1. 10" 
2-2 .  10" 
3-2.10" 

Mean  =  2-5 .  104 


In  order  to  calculate  the  concentration  of  Hg  ••  ions,  the 
concentration  of  these  in  the  normal  calomel  electrode  was 
taken  as  5*3  x  10 -20  gram  ions  per  litre.  The  method  by 
which  this  value  was  arrived  at  will  be  given  in  a  later 
chapter  (see  Chapter  X).  Difficulty  was  experienced  in 
making  the  measurements,  as  the  E.M.F.'s  did  not  remain 
perfectly  constant. 

Applying  the  Bodlander  method  to  the  results  we  obtain 
r  =  4,  but  the  value  of  q  is  less  than  the  minimum  of  1. 
From  the  constancy  of  the  values  in  the  last  column,  however, 
it  is  evident  that  the  main  quantity  of  complex  ions  present 
must  have  the  formula  Hg(CJSr)4". 

The  solutions  used  in  these  experiments  all  contained  a 


SOME   EXAMPLES  55 

considerable  excess  of  potassium  cyanide.  In  order  to  see 
whether  complex  ions  containing  less  cyanogen  would  be 
formed  under  different  circumstances,  a  method  was  worked 
out  by  which  this  information  could  be  obtained  from 
potential  measurements  with  solutions  saturated  with 
mercuric  cyanide. 

In  this  case  we  have  an  additional  unknown  quantity  to 
deal  with,  namely,  the  concentration  of  the  cyanogen  ions. 
This  can  be  obtained  at  the  expense  of  one  of  the  indices  in 
the  equation  for  equilibrium. 

We  shall  consider  the  dissociation  of  the  complex 
according  to  the  following  scheme : — 

mHg(CN)2,  (CN')n^mHg"  +  (2m  +  »)CN' 

whence  LH8»(C-")8»+»]    _  j- 

[Hg-]m[C]Sf']2m  +  w 

Let  a  be  the  concentration  of  the  alkali  cyanide.  Then 
the  concentration  of  the  complex  Hgm(CN)2m  +  n  is  given  by 

-.     Thus 
n 

a 

n 


K  = 


Considering  two  solutions  we  obtain 

aA      [HgjACN^2"^ 
«*      [Hgi2™[CN']22™  +  n 
Since    the    solutions    are    saturated    with    respect    to 
Hg(CN)2,  the  solubility  product  [Hg-][CN']2  is  a  constant, 

and  therefore 

[Hy-h  _  [CNV 
[Hg"]«      [ON'J!- 


2 

1 

2m  +  n 


<h  _  rHS-ir[Hgj2  « 

Hence  2m  + « 

a*   [Hg-rtHg-ii-f- 

.  (*4  _  [Hg"]i 


56 


COMPLEX  IONS 


The  E.M.F.  of  the  concentration  cell  containing  the  two 
solutions  is 

E  =  0-0295  logffi"]1 
8  [Hg-]2 

Substituting  from  the  previous  equation  we  get 

0-059,     a2 

n  =    ,,    log  — 

E       &«i 


or 


_      0*059,     a2 

E  = log^ 

n       °a1 


We  can  thus  find  n,  but  not  m. 
The  E.M.F.  of  the  cell 

00985  N.  KCN 
Sat.  with  Hg(CN)2 


Hcj 


0-197  N.  KCN 
Sat.  with  Hg(CN)2 


Her 


was  found  to  be  0*016  volt.  Putting  n= 1  and  calculating  the 
E.M.F.,  we  find  E  =  0*017 ;  or,  calculating  n,  we  get  n  =  1*05. 

It  thus  appears  that  when  Hg(CN)2  is  in  excess  the 
complex  ion  Hg(CN)3'  is  formed  at  the  expense  of  the  ion 
Hg(CN)4". 

The  cryoscopic  method  was  next  applied,  the  effect  of  the 
addition  of  Hg(CN)2  to  solutions  of  KCN  upon  the  freezing 
point  being  observed.  The  following  table  shows  the  results 
obtained : — 


Cone.  KCN. 

Total  cone. 
Hg(CN)2. 

Increase  in 
cone,  of 
Hg(CN)2. 

Freezing  point. 

Rise  in 
freezing  point. 

Rise  -^  1-85 

=  diminution  in 

gram  mols.  per 

litre. 

0-1965 
0-1965 
0-1965 
0-1965 
0-1965 

000 

0-0476 

0-0953 

0-1905 

0-3910 

0-0476 
0-0476 
0095 
0-191 

-0-704 
-0-608 
-0-534 
-0-678 
-0-990 

0096 

0-074 

-0144 

-0-312 

0-052 
004 

-  0078 

-  0168 

0-50 
0-50 
0-50 
0-50 
0-50 
0-50 

0-00 
0-21 
0-30 
0-36 
0-42 
0-50 

0-21 
0-09 
006 
0-06 
0-08 

-1-745 
-1-280 
-1-296 
-1-410 
-1-507 
-1-653 

0-465 
-0016 
-0-114 
-0-097 
-0-146 

0-25 
-0009 
-0062 
-0-052 
-0-079 

From  these  values  we  may  draw  the  following  conclusions  :■ 


SOME  EXAMPLES  57 

During  the  addition  of  Hg(CN)2  to  the  solution,  for  each 
molecule  of  Hg(CN)2  added  the  solution  contains  one  mole- 
cule less,  that  is,  two  ON'  ions  must  disappear  for  each 
Hg(CN)2  molecule  added.  This  continues  until  the  solution 
contains  half  a  molecule  of  added  mercuric  cyanide  for  each 
molecule  of  potassium  cyanide.  From  this  point  onwards 
addition  of  Hg(CN)2  causes  a  lowering  of  the  freezing  point 
corresponding  to  an  increase  in  the  number  of  molecules  per 
litre  which  is  equal  to  the  number  of  molecules  of  Hg(CN)2 
added. 

This  latter  behaviour  may  be  the  outcome  of  either  or 
both  of  two  states  of  affairs  in  the  solution.  Either  (1)  the 
added  Hg(CN)2  remains  unchanged  or  (2)  it  reacts  with 
the  Hg(CN)4"  ions  already  present  according  to  the  scheme 

Hg(CN)4"  +  Hg(CN)2  =  2Hg(CN)3' 

From  the  results  obtained  from  the  potential  measurements 
it  will  be  seen  that  the  latter  process  must  be  regarded  as 
occurring  to  a  considerable  extent  at  least.  This  point  was 
further  investigated  by  determining  the  solubility  of 
Hg(CN)2  in  KCN  solutions. 

If  the  first  state  of  affairs  mentioned  above  were  that 
actually  existing,  the  only  reaction  occurring  would  be  that 
represented  by  the  equation 

Hg(CN)2  +  2CN'  =  Hg(CN)4" 

The  increase  in  solubility  of  the  mercuric  cyanide  should 
therefore  be  equal  to  half  the  concentration  of  the  potassium 
cyanide.  On  the  other  hand,  if  the  solution  behaves  accord- 
ing to  the  second  scheme,  the  increase  in  the  solubility  of  the 
mercuric  cyanide  must  be  greater  than  half  the  concen- 
tration of  the  KCN ;  and  if  the  formation  of  the  complex 
Hg(CN)3'  were  complete  in  the  saturated  solution,  the 
increase  in  the  solubility  would  be  equal  to  the  concentration 
of  KCN. 

The  solubility  of  Hg(CN)2  in  water  was  found  to  be  0*44 
gram  molecule  per  litre  at  25°.      The  following  table  shows 


58 


COMPLEX   IONS 


the  solubility  in  three  solutions  of  KCN  and  the  increase 
over  the  solubility  in  water : — 


Cone.  KCN. 


Solubility  of  Hg(CN)2.  j  Increase  in  solubility. 


OOO 

0-44 

00493 

0-4855 

00985 

0-5350 

0-1970 

0-627 

0  0455 

0095 

0-187 


Since  the  increase  in  solubility  is  actually  nearly  equal 
to  the  concentration  of  KCN,  it  follows  that  the  formation 
of  the  complex  ion  Hg(CN)3'  in  solutions  saturated  with 
Hg(CN)2  is  nearly  complete.  Since  the  dissociation  of 
mercuric  cyanide  in  solution  is  exceedingly  small,  the 
depression  of  solubility  caused  by  the  potassium  cyanide  is 
quite  negligible. 

On  account  of  the  high  stability  of  the  complex  Hg(CN)3', 
it  is  not  possible  to  examine  its  dissociation  by  any  method 
except  that  of  potential  measurements.  Its  formation  in 
strong  solutions  of  Hg(CN)2  in  KCN,  however,  was  further 
investigated  by  means  of  distribution  measurements. 

Aqueous  solutions  of  potassium  cyanide  containing 
Hg(CN)2  were  shaken  with  ether,  and  the  distribution  ratio  of 
the  Hg(CN)2  between  the  two  liquids  was  determined.  The 
accompanying  table  shows  the  values  found : — 


Cone.  KCN. 

Conc.Hg(CN)2in 
aqueous  layer. 

FreeHg(CN)2in 
aqueous  layer. 

Cone.  Hg(CN)2  in 
ether. 

Distribution 
coefficient. 

000 

0-0493 

00493 

0-0493 

0-0493 

0-44 
0-410 
0-370 
0-300 l 
0-274 

0-44 

0-361 

0-321 

0-251 

0-225 

001 

0-00785 

0-00685 

0-00567 

000413 

44 
46 
47 
44 
44 

The  concentration  of  free  Hg(CN)2  in  the  aqueous  layer  was 
obtained  by  subtracting  the  concentration  of  KCN  from  that 
of  the  total  Hg(CN)2,  that  is,  by  assuming  the  complete  for- 
mation of  the  complex  ion  Hg(CN)3\ 

1  Given  as  0-200  in  the  original. 


SOME  EXAMPLES  59 

The  fact  that  the  distribution  coefficient  calculated  in 
this  way  remains  constant  and  has  the  same  value  as  that 
obtained  for  the  saturated  solution  in  absence  of  KCN  affords 
strong  evidence  in  corroboration  of  that  obtained  in  the 
previous  experiments  for  the  formation  of  the  complex  ion 
Hg(CN)3'.  It  must  be  added,  however,  that  this  set  of 
experiments,  taken  alone,  would  have  carried  more  weight 
if  determinations  of  the  distribution  coefficient  had  been 
made  in  absence  of  KCN  over  the  range  of  concentrations 
given  for  the  free  Hg(CN)2  in  order  to  gain  assurance  that 
the  coefficient  really  is  independent  of  the  concentration. 

Experiments  similar  to  the  above  were  carried  out  with 
solutions  of  Hgl2,  HgBr2,  and  HgCl2  in  solutions  of  the  cor- 
responding alkali  halides.  In  the  case  of  these  salts,  a 
saturated  solution  in  contact  with  mercury  cannot  exist,  as 
the  corresponding  mercurous  compound  is  precipitated,  and 
the  E.M.F.  measurements  could  not  therefore  be  extended  to 
these.  A  long  series  of  E.M.F.  measurements  showed  that 
in  solutions  which  did  not  contain  a  great  excess  of  KI,  a 
complex  was  formed  which  contained  less  than  two  added 
iodine  ions.  Distribution  experiments  by  Dawson  {Trans. 
Chem.  Soc,  95,  870  (1909))  also  led  to  this  result.  In  each 
case  Sherill  concluded  that  a  complex  ion  of  the  type  HgX4" 
was  mainly  formed,  but  Sand  and  Breest  (ZeiL  phys.  Chem., 
59,  424  (1907))  have  shown  that  Sherill's  distribution 
experiments  in  the  cases  of  mercuric  bromide  and  chloride 
can  be  better  interpreted  by  assuming  the  formation  of 
the  ion  HgX3'. 

One  other  set  of  Sherill's  measurements  may  be  men- 
tioned as  noteworthy.  These  depended  upon  the  rate  of 
catalysis  of  the  decomposition  of  hydrogen  peroxide  by 
iodine  ions,  which  had  previously  been  measured  by  Bredig 
and  Walton  (Zeit.  Mehtrochem.,  9,  114  (1903)).  Bredig  and 
Walton  showed  that  the  speed  of  decomposition  was  pro- 
portional to  the  concentration  of  iodine  ions.  By  observing 
the  speed  of  decomposition  induced  by  the  complex  solution, 
the  concentration  of  the  iodine  ions  in  it  could  be  determined. 


60 


COMPLEX   IONS 


On  subtracting  this  from  the  total  concentration  of  potassium 
iodide  in  the  solution  (assuming  complete  dissociation)  we 
find  the  concentration  of  iodine  ions  present  as  complex,  and 
since 

mHgI2  +  nV  m  (HgI2)mV 

on  dividing  the  concentration  of  "  bound  "  iodine  ions  by  the 


concentration  of  Hgl2  we  obtain  the  ratio  - 
ing  table  shows  the  results  obtained : — 


The  follow- 


.  KI.      Cone.  Hgl2. 

K  =  velocity 
constant. 

Cone.  I'. 

Cone, 
"bound"  I' 

Cone.  "  bound  "  I' 

Cone 

Cone.  Hgl2 
n 
—  m 

o-o: 

J125        000 

004145 

003125 

000 

000205 

003639 

0-0274 

00039 

1-9 

000397 

0-03241 

00244 

00069 

1-74 

0-00547 

0-0286 

0-0215 

0-0097 

1-77 

0-00798 

0-02326 

00176 

00136 

1-70 

001017 

0-01856 

001395 

0-0173 

1-70 

0-01078 

0-01775 

0-0134 

0-0178 

1-65 

001161 

001665 

001255 

0-0187 

1-61 

0-01315 

0-01453 

001094 

0-0203 

1-54 

Thus  it  appears  that  while  in  solutions  that  are  weak  with 
respect  to  Hgl2,  such  as  were  used  for  the  E.M.F.  measure- 

ments,  —  is  practically  2,  the  value  of  this  ratio  continually 

falls  as  the  amount  of  Hgl2  in  solution  increases.  Another 
similar  set  of  measurements  made  with  solutions  of  various 
concentrations  of  KI,  and  saturated  with  respect  to  Hgl2 

gave  values  of—  ranging  from  1*63  in  0*23  N".  KI  to  1*50  in 

0-018  N.  KI. 

Freezing-point  experiments  showed  that  for  every 
molecule  of  Hgl2  introduced,  the  total  number  of  molecules 
in  solution  was  diminished  by  one.  This  can  only  be 
explained  by  assuming  the  formation  of  Hgl4"  according  to 
the  equation 

Hgl2  +  21'  =  Hgl4" 


SOME   EXAMPLES  61 

and  not,  as  Sherill  supposed,  by  the  formation  of  a  complex 
of  the  general  type  (Hgl^I'^  + 1,  which  would  only  cause 
the  concentration  to  fall  by  one  gram  molecule  per  litre  for 
the  addition  of  x  gram  molecules  of  Hgl2.  Sherill's  assump- 
tion of  the  formation  of  the  complex  ion  (Hgl^^V  is  there- 
fore based  upon  an  error  so  far  as  freezing-point  experiments 
are  concerned.  The  evidence  for  the  formation  of  this 
compound  must  be  regarded  as  very  slight,  since  another 
interpretation  can  be  placed  upon  the  experiments  on  the 
catalysis  of  the  decomposition  of  hydrogen  peroxide  and 
Dawson's  results,  namely,  the  partial  formation  of  the  ionHgI3\ 

The  existence  of  the  complex  ions  HgBr/'  and  HgCl*" 
was  shown  in  a  manner  similar  to  the  above.1 

In  illustration  of  the  direct  solubility  method  of  attacking 
these  problems,  which  in  Sherill's  work  did  not  give  simple 
results,  we  may  quote  the  results  of  an  investigation  by  Pick 
{Dissert.,  Breslau,  1906 :  Zeit.  anorg.  Chem.,  51,  1  (1906))  of 
solutions  of  silver  nitrite. 

Measurements  of  the  E.M.F.  of  the  cell 

Ag  |  KN02  +  AgN02  sol.  |  01  N.  KN02 1  01  N.  E. 

showed  that  in  the  scheme 

2Ag-+rN02'^Ag2(N02')r 

q  =  1  and  r  =  2,  and  a  very  concordant  set  of  values  was 
calculated  for  the  constant 

_  [Ag-][N02'P 
*  ~  [Ag(N03V] 

using  the  known  electrolytic  potential  of  silver.  These  gave 
the  mean  value  of  kx  as  1'47  X  10~3. 

These  results  were  checked  by  means  of  solubility 
measurements,  and  the  constant 

_   [Agm(NQ2)m  +  n] 
2  "  [AgN02]™[N02']« 

was  calculated  on  the  assumption  that  m  —  1   and  n  =  1. 

1  But  see  Sand  and  Breest  (loc.  cit). 


62  COMPLEX   IONS 

Following  the  method  of  Sherill,  we  see  that  in  saturated 

solutions    the  concentration   [AgN02]    (=  b)    is   constant, 
whence 


[Agm(N02) 


m  +  n] 


=  koXb 


m 


[N02']» 

If  the  total  silver  content  of  the  solution  be  determined  and 
have  the  value  x,  then 

x  -  b  -  [Ag-]  =  c 
c  being  the  concentration  of  silver  atoms  present  as  complex, 
corresponding  to  the  complex  concentration  — .  The  solu- 
bility product  of  silver  nitrite  had  been  determined  pre- 
viously, and  found  to  have  the  value  2*0  X  10 -4  at  25°. 
Calculating  the  silver  ion  concentrations  in  the  solutions 
used  (see  table),  we  find  that  the  term  [Ag*]  may  be  neglected 
in  the  above  equation,  so  that  we  may  write,  with  a  sufficiently 
good  approximation  to  the  truth, 

x  —  b  =  c 
The  concentration  of  nitrite  ions  contained  in  the  form  of 

complex  is  — .  c.     Hence,  if  a  be  the  initial  concentration  of 
m 

N02-ions,  we  get  when  the  system  is  in  equilibrium 

a  -  * .  e  m  [N02'] 
m  L         J 


Hence  kJ 


c 
m 


2 

m 


(a c) 


a  —  c  is  given  by  subtracting  twice  the  total  silver  concentra- 
tion, less  b,  from  the  total  nitrite  ion  concentration,  on  the 
assumption  that  m  =  n  =  1,  and  again  neglecting  the  pre- 
sence of  silver  ions.  As  b  is  always  very  small  compared 
with  a  —  c  in  the  solutions  used,  Pick  neglected  it  also. 
This  quantity,  a  —  c,  representing  the  total  nitrite  ion 
content,  does  not  take  account  of  the  undissociated  added 


SOME   EXAMPLES 


63 


salt,  and  must  accordingly  be  multiplied  by  a,  its  degree  of 
dissociation. 

The  solubility  of  silver  nitrite  was  accordingly  deter- 
mined in  barium  nitrite  solutions,  the  values  of  a  being 
taken  from  the  conductivity  measurements  of  Vogel  {Zeit. 
anorg.  Chem.,  35,  407  (1903)). 

The  nitrite  content  of  the  solutions  was  determined  by 
titration  with  potassium  permanganate,  and  the  silver  con- 
centration by  Volhard's  method.  The  results  are  given  in 
the  following  table  : — 


Titration  concentrations. 

N02-2Ag 
=  a  -c. 

[N02'J 
=  (a  -  c)a. 

Ag  -  b  =  c. 

j  .         c 

kz  -  (a  -  c)a 

N02. 

Ag. 

0-9921 

00625 

0-8761 

0-525 

0-0508 

0-097 

0-8609 

00554 

0*7501 

0-473 

0-0437 

0-092 

0-8100 

00495 

0-7020 

0-449 

0-0378 

0-084 

0-5822 

0-0379 

0-5064 

0-355 

0-0262 

0-074 

0-4876 

0-0327 

0-4222 

0-310 

00210 

0-068 

0-3089 

0-0239 

0-2611 

0-209 

0-0122 

0-058 

0-2020 

0-0202 

0-1616 

0-132 

0-0085 

0-064 

01134 

0-0173 

0-0788 

0-0678 

0-0056 

0-083 

Mean  =  0*077 


It  cannot  be  said  that  the  constant  exhibits  a  very  high 
degree  of  constancy,  but  it  may  fairly  be  claimed  that  it  is 
much  more  constant  for  ra  =  n  =  1  than  for  any  other 
values  of  these  two  coefficients ;  and  it  is  to  be  remembered 
that  a  large  number  of  experimental  data  is  used  in  the 
calculation. 

Few  cases  have  been  investigated  in  which  the  solubility 
and  dissociation  of  the  "  neutral  part  "  are  such  that  the  free 
ions  produced  by  the  dissociation  cannot  be  neglected,  and 
which  thus  require  rigorous  mathematical  treatment  based 
upon  the  principles  given  in  Chapter  V. 

W.  K.  Lewis  (Dissert.,  Breslau,  1908)  worked  out  the  case 
of  the  nitrates  of  lead  and  potassium,  each  of  which  shows  a 
greatly  increased  solubility  in  presence  of  the  other.     The 


64  COMPLEX   IONS 

results  appear  to  indicate  the  formation  of  a  complex  kation 
of  the  formula  KPbN03",  or,  at  least,  as  Lewis  says,  "  can 
be  interpreted  qualitatively  and  quantitatively  within  the 
limits  of  experimental  error  "  by  assuming  the  existence  of 
this  ion.  The  main  evidence  for  the  presence  of  potassium 
in  the  ion  is  the  fact  that  sodium  nitrate  behaves  normally 
with  lead  nitrate,  that  is,  the  two  salts  exert  a  mutually 
depressing  influence  upon  their  respective  solubilities. 

Unfortunately  the  saturated  solutions  of  these  salts  are 
so  concentrated  that  the  law  of  mass  action  cannot  be 
regarded  as  applying  at  all  in  a  quantitative  sense,  and  the 
mathematical  investigation  was  confined  mainly  to  measure- 
ments of  electrode  potentials  in  weaker  solutions.  The 
theoretical  treatment  of  these  measurements  may  be 
noticed. 

We  may  assume  that  lead  nitrate  dissociates  in  two 
stages  according  to  the  scheme 

Pb(N03)2^PbN03-  +N03' 
PbN03-    ^Pb-  +  N03' 

The  extent  of  the   dissociation  at  each  stage  is  therefore 
determined  by  the  equations 

_  [PbNCV][NCy] 

*•  -  •  [Pb(No3)2r   •  •  •  •  w 


_  [Pb"][N03'] 
A2~    [Pbao,-] 


(2) 


In  any  solution,  whether  containing  added  alkaline 
nitrate  or  no,  the  total  concentration  of  lead  nitrate,  c,  is 
given  by 

c  =  [Pb-]  +  [PbN03-]  +  [(PN03)J  .     .     (3) 

In  a  pure  solution  of  lead  nitrate  we  have,  further,  since  the 
solution  is  electrostatically  neutral,  the  relation 

2[Pb"]  +  [PbN03«]  =  [N03'J  ...     (4) 

From  (2)  and  (4)  by  elimination  of  [PbN03*]  we  obtain 


^=Sfe <5> 


SOME   EXAMPLES  65 

From  (3)  and  (4)  we  may  find  [Pb(N03)2]  in  terms  of  e, 
[Ptr]  and  [N03'],  and  obtain 

[Pb(N03)2]  =  c  -  [N03']  +  [Pb"] 

Multiplying  equations  (1)  and  (2)  together  and  substituting 
for  [Pb(ISr03)2],  we  find 


-1^2 


-SS+[Pbi 


[N03']  +  [Pb- 
Substituting  for  [N"03'J,  we  get 

r      /  2[Pb-]K2  y 

~K2-[Pb"] 
which  reduces  to  the  quadratic  equation  in  K2 

K2\e  -  [Pb"])  -K2(C  +  ^l2)2[Pb"] 

+  [Pb"]2(c  +  [Pb"])  =  0 (6) 

2rPb**l2 
It  can  be  shown  by  trial  that    L.~    J    is  small   enough 
*  Kj  ° 

to  be  neglected  in  comparison  with  c,  and  we  thus  obtain  an 
equation  giving  K2  in  terms  of  c  and  [Pb"],  which  is  likely  to 
prove  of  value  in  future  investigations  of  ternary  electrolytes. 
If  we  have  two  solutions  of  lead  nitrate  and  find  the 
ratio  of  the  concentrations  of  lead  ions  in  them  by  means  of 
potential  measurements,  then  obviously  we  are  in  a  position 
to  find  K2  by  trial,  remembering  that  K2  is  a  constant. 
This  method  was  used  by  Jaques  (loc.  cit.)  in  investigating 
the  equilibria  in  solutions  of  lead  acetate  and  cadmium  acetate 
in  alkali  acetates.  Lewis  proceeded  to  make  further 
approximations  in  the  above  equation  (which  we  may  refer 
to  as  "  Lewis's  equation  "),  and  combined  it  with  the  Nernst 
equation 

.  =  0-0295  log|£i 

so  as  to  obtain  a  direct  solution.    For  details  of  these  further 
calculations  the  reader  should  consult  the  original  paper. 


F 


66 


COMPLEX   IONS 


A  provisional  value  of  K2  was  thus  found.  The  following 
table  reproduces  Lewis's  results,  [Pbr]  in  0*01  molar  solution 
being  taken  as  0'0087  :— 


c. 

K2. 

o-oi 

0-128 

0-05 

0-088 

0-25 

0-103 

0-4 

0-108 

1-0 

0-126 

In  the  case  of  a  solution  containing  added  alkaline 
nitrate,  equation  (4)  no  longer  holds.  From  equations  (1), 
(2),  and  (3)  we  obtain  by  elimination  of  [PbN03*]  and 
[Pb(N03)2] 

rpb-i  = KlK2C n\ 

LrD  J      [N03']2  +  KiK2  +  Ki[NOal       '     K'} 

This  equation  should  hold  for  both  the  pure  solution  of  lead 
nitrate  and  solutions  containing  alkaline  nitrate. 

Inserting  the  value  found  for  K2  in  the  above  equation,  and 
using  equation  (5)  in  the  case  of  pure  lead  nitrate  solutions, 
we  can  now  find  the  value  of  Kr  Lewis  gives  the  following 
table  of  values  obtained  in  this  way : — 


c. 

Con< 

:.  NaN03. 

Ki. 

0-01 

o-i 

0-15 

0-01 

1-0 

0-15 

0-05 

— 

Oil 

0-25 

— 

0-33 

0-40 

— 

0-46 

1-0 

— 

4-0 

As  Ki  increased  rapidly  with  increase  in  c,  Lewis  plotted 
Kx  against  c,  and  found  that  the  values  of  Kx  with  the 
exception  of  the  last  one  could  be  expressed  empirically  as  a 
linear  function  of  c,  namely 


Ki  =  0-14  x  0-77c 


SOME   EXAMPLES 


67 


Lewis  now  substituted  the  right-hand  side  of  this  expression 
in  his  equation,  and  showed  that  the  expression  thus  obtained 
for  [Pb,#]  in  terms  of  c  and  K2  gave  values  of  [Pb**]  which 
agreed  excellently  with  those  obtained  by  direct  potential 
measurements.     This  is  shown  by  the  following  table  : — 


c. 

NaN03. 

e. 

I. 

II. 

AMV. 

1-0 

-0-439 

0-089 

0-083 

1 

0-4 

— 

-0-443 

0-065 

0-065 

0 

0-25 

— 

-0-445 

0-056 

0056 

0 

005 

— 

-0-455 

0-0255 

0-0258 

0 

001 

1-0 

-0-511 

0-000324 

000033 

0 

o-oi 

0-1 

-0-479 

0-0039 

0-0042 

1 

001 

— 

-0-469 

0-0083 x 

0-0083  l 

— 

e  is  the  potential  of  the  lead  electrode  with  respect  to  the 
1*0  K  calomel  electrode  at  25°.  In  Column  I.  are  given  the 
values  of  [Pb"]  calculated  from  the  potential  by  means  of  the 
formula 

e  =  -0-408  +  0-0295  log  [Pb"] 

In  Column  II.  are  the  values  calculated  by  means  of  the 
substituted  equation  connecting  [Pb**]  and  c,  or,  in  the  cases 
where  NaN03  is  present,  from  equation  (7).  The  difference 
in  the  last  column  is  reckoned  in  millivolts. 

Having  thus  obtained  a  satisfactory  means  of  calculating 
[Pb-],  [PbNCV],  and  [Pb(N03)2]  in  any  solution  from  a 
knowledge  of  the  potential  of  a  lead  electrode  dipping  into  it, 
Lewis  proceeded  to  the  study  of  the  complex  solutions 
obtained  by  mixing  lead  nitrate  with  potassium  nitrate. 

The  total  lead  concentration,  c,  may  be  split  into  the 
"normal"  concentration,  cn,  and  the  complex  lead  concentra- 
tion, C,  so  that 

e  -  cn  +  0 

where  cn  =  [Pb-]  +  [PbN03-]  4-  [Pb(N03)2] 

cn  was  found   from  the   potential  by  the   method  sketched 

above,  and  C  was  then  given  by 

C  =  e-en 

1  Starting  point  of  the  calculation.     These  values  were  taken  as  equal. 


68  COMPLEX   IONS 

Thus  we  now  have  numerical  values  for  [Pb,#],  [N03'],  and  C 
and  the  constitution  of  the  complex  can  be  decided  by  th 
method  of  Bodlander,  with  the  one  reservation  that  it  woul 
be  difficult  to  make  two  solutions  in  which  [N03']i  was  no 
equal  to  [N03']2,  while  Ci  was  equal  to  C2.     The  law  of  mass 
action  was  therefore  applied  in  this  way  :   that  the  dissociation 
constant 

Aa  -    py>b5(No8)j     •   •   •  •  K> 

was  calculated  for  various  values  of  p,  q,  and  r,  and 
the  values  of  these  indices  were  thus  found  which  gave  the 
best  constancy  of  K3.  All  the  measurements  were  made 
with  solutions  in  which  the  potassium  nitrate  was  in  large 
excess  compared  with  the  lead  nitrate,  so  that  [K*]  could  be 
set  equal  to  [N03'].  The  results  appear  to  show  that  p,  q,  and 
r  are  each  equal  to  1,  though  unfortunately  the  constancy  of 
K3  was  in  no  case  very  satisfactory.  The  mean  value  was 
taken  as  0*036. 

Using  the  numerical  values  of  Ki,  K2,  and  K3,  we  can 
calculate  theoretically  the  concentration  of  lead  ions  in  any 
mixture  of  lead  and  potassium  nitrates,  and  by  comparing 
these  with  the  values  found  by  measurements  of  the  poten- 
tial of  the  lead  electrode  we  can  thus  check  the  accuracy 
of  our  conclusions.  The  calculation  is  carried  out  as 
follows : — 

For  the  mixed  solution  the  following  equations  hold  : — 

_  [PbNCV][N03']  _ 
Kl_      [Pb(N03)2]      -Ui4  +  »"c      •     W 
_  [Pb-][N03-]  _ 

K*~     [PbNOy]    -011 (2) 

_  [Pb"][NOa'][K-] 

K3~      [PbN03K-]     -00°6 (8) 

[PbN03K-]  +  [Pb-]  +  [PbN(V]  +  [Pb(NOs)2]  =  e ,     (9) 
Combining  tbese  we  obtain 


[Pb"1 "  [k-p<v]  .,  [n4i» ;  [m<vj  ;    <10> 


Ivq  KiKo  k 


1JV2 


SOME   EXAMPLES  69 

The  values  of  [Pb*]  in  a  number  of  mixed  solutions  in 
which  the  concentrations  of  the  two  salts  varied  between 
wide  limits  were  calculated  by  means  of  equation  (10),  and 
showed  very  close  agreement  with  the  values  obtained  by 
potential  measurements,  the  difference  between  the  two 
values  in  no  case  amounting  to  more  than  two  milli- 
volts. 

It  was  also  shown  that  the  general  behaviour  of  the 
solubilities  was  such  as  to  support  the  foregoing  conclusions, 
namely,  that  in  mixed  solutions  of  lead  and  potassium 
nitrates  the  complex  ion  [PbNOaK"]  is  formed. 

A  somewhat   similar  method   of  attack   was   used  by 

Jaques  (loc.  cit.)  in    investigating  the   complex   formation 

occurring  in  solutions  of  lead  and  cadmium  acetates.     In 

each  case  K2  was  determined  from  potential  measurements 

by  means  of  Lewis's  equation,  and  it  was  found  by  means  of 

freezing-point  experiments  that  ~K±  was  sufficiently  large  to 

2rPb"l2 
ensure  that    L^    J   could  be  neglected  in  comparison  with  c, 

Ki  was  found  more  accurately  by  the  solubility  method, 
using  the  value  of  K2  already  found.  Since  both  lead  and 
cadmium  acetate  are  too  soluble  to  allow  of  the  application 
of  the  law  of  mass  action  to  their  own  solubilities,  the 
method  was  reversed,  and  the  solubility  of  silver  acetate, 
which  is  small,  was  determined  in  solutions  of  the  two  salts 
to  be  experimented  upon.  Measurements  of  the  solubility 
of  silver  acetate  in  solutions  of  sodium  and  potassium  acetates 
showed  that  silver  acetate  does  not  form  complex  ions  with 
additional  acetate  ions  that  may  be  present  to  any  measurable 
extent. 

The  calculation  of  Kx  is  carried  out  as  follows : — 

We  have  first 


[PbAc][Ac]  _ 

[PbAcJ            *      '    " 

•     •    (1) 

[Pb"][Ac']  _ 
[PbAc]    -Ka-    •    • 

•     •     (2) 

70  COMPLEX   IONS 

Next,  calling  the  solubility  of  silver  acetate  in  a  lead  acetate 
solution  r)}  we  have 

n  +  2c  =  [AgAc]  +  [PbAc]  +  2[PbAc2]  +  [Ac']  .     (3) 

Also,  since  the  solution  is  electrostatically  neutral 

[Ag-]  +  [PbAc]  +  2[Pb~]  =  [Ac']  .  .  (4) 
From  (2)  and  (4) 

[Ac']-[Ag-]  =  [PbAc](l+^) 

whence  [PbAc]  =  ^  ~}^    ....     (5) 

14- 


[Ac'] 
From  (3) 

[pbAc2]  m  r>  +  2c-  [AgAc] -[PbAc]-  [Ac'] 

We  thus  find  [Pb"],  [PbAc],  and  [PbAc2]  in  terms  of 
[Ac'],  [AgAc],  and  [Ag*].  These  latter  values  are  found  by 
determining  the  molecular  electrical  conductivity  A,  of  the 
silver  acetate  in  saturated  solution  in  water,  and  using  the 
values  given  by  Loeb  and  Nernst  (Zeit.  phys.  Chem.,  2,  948 
(1888))  for  its  conductivity  at  infinite  dilution,  Ax.  y,  the 
degree  of  dissociation,  is  given  by 

A 

and  [Ag-]  by 

[Ag-]  =  ys 

where  s  is  the  solubility  of  the  salt  in  water.  The  solubility 
product,  L,  is  found  from  the  equation 

L  =  (ysf 

and  the  value  of  the  concentration  [AgAc]  is  obtained  from 
the  equation 

[AgAc]  =  s  -  [Ag-] 

L  and  [AgAc]  are  constant  in  all  saturated  solutions,  and  we 
may,  therefore,  use  the  values  we  have  found  in  investigating 
the  solutions  containing  lead  or  cadmium  acetate. 


SOME  EXAMPLES  71 

Dealing  now  with  the  mixed  solutions,  we  have 
[Ag*]  =  »,  -  [AgAc] 

and  [Ac'  I  =  j^ — =i 

L      J      [Ag-] 

We  are  thus  in  a  position  to  obtain  numerical  values  for 

[PbAc*],  [Ac'],  and  [PbAc2J  in  the  mixed  solutions,  and  can, 

therefore,  calculate  the  value  of  Ki  from  equation  (1).     The 

accompanying  table  shows  the  results  obtained,  using  the 

values  [AgAc]  =  0*0172  and  L  =  0*00242. 


c(lead 
acetate). 

n- 

t)  -  [AgAc] 
=  [Ag\). 

^=[AC]. 

[PbAc-]. 

[PbAc2]. 

Kl 

10 
0-5 
01 
0-05 

o-oi 

0-03587 

004349 

004995 

0-0566 

006403 

0-01867 

0-02631 

003275 

00394 

0-0468 

0-1297 
00921 
0-0739 
0-0614 
00517 

fc—  CO  OS  O  3 

88S88 

6666  6 

ooooo 

at  oo  co  en  o 
oo  <j5  co  as  c5 
o 

00157 
00133 
0-0482 
00444 
00441 

The  last  three  values  of  Ki,  i.e.  those  obtained  in  dilute 
solutions,  show  a  fair  degree  of  constancy.  All  work  of  this 
kind  suffers  from  the  large  number  of  experimental  values 
that  have  to  be  introduced  into  the  calculations. 

The  mean  value  of  Kx  was  now  substituted  in  Lewis's 
equation,  which  was  solved  without  approximation  for  K2, 
with  the  result  that  K2  was  found  to  have  the  value  0*0021 
instead  of  0*0020,  the  provisional  value  used  in  calcu- 
lating Ki. 

As  in  Lewis's  work,  the  calculations  were  now  applied  to 
the  complex  solutions,  and  the  concentration,  C,  of  the  lead 
present  as  complex  was  determined. 

The  values  of  q  and  r  in  the  equation 

[Pb-HAcT  _ 
[Pb3Acr]    ~^3 

were  now  calculated.  These  had  already  been  worked  out 
by  means  of  Bodlander's  theorem,  on  the  assumption  that 
all  the  lead  was  in  the  form  of  the  complex  ion.  q  was 
found  to  be  1,  while  r  varied  rapidly  with  the  concentration 


72  COMPLEX   IONS 

of  the  alkaline  acetate.  It  was  now  found  that  in  solutions 
of  equal  acetate  ion  concentration  C  was  proportional  to  c, 
so  that 

[PbAcr]i      C_r=  ci 

[PbAcr]2  ~~  C2      c2 

Thus  the  value  of  q  is  unaffected  by  taking  into  consideration 

the  incompleteness  of  the  complex  formation,  but  the  value 

of  r,  on  the  other  hand,  is  considerably  affected. 

Instead  of  calculating  the  constant  K3  for  various  values 
of  r  (q  beiug  known  to  be  1),  the  method  of  Bodlander  was 
extended  in  the  manner  described  in  Chapter  VI  to  the  case 
where  [PbAcJi,  [PbAcr]2,  [Ac']i,  and  [Ac']2  are  all  unequal. 

In  the  case  of  lead  acetate  the  values  of  r  increased 
rapidly  with  increasing  acetate  ion  concentration,  but  even 
in  the  more  dilute  solutions  (0*279  and  0*673  N.  solutions 
of  sodium  acetate)  the  values  lay  between  3  and  4.  If 
we  plot  r  against  the  mean  value  of  [Ac']i  and  [Ac']2  we 
find  that  when  [Ac']i  and  [Ac']2  become  indefinitely  small, 
r  becomes  approximately  3.  Thus  the  ion  PbAc'3  is  pro- 
bably formed,  and  possibly  an  ion  or  ions  containing  more 
acetate  ions  such  as  PbAc4",  but  the  high  values  of  r  in  the 
strong  solutions  of  alkali  acetate  must  be  regarded  as  pro- 
bably due  to  disturbing  influences  such  as,  possibly,  hydrate 
formation.     (See  Appendix  I.) 

The  behaviour  of  cadmium  acetate  solutions  was  precisely 
similar. 

For  an  examination  of  mixed  solutions  of  zinc  and 
mercuric  chlorides,  and  of  the  dissociation  of  zinc  chloride, 
barium  chloride  and  barium  bromide,  the  reader  is  referred 
to  Drucker,  Zeit.  Elehtrochemie,  18,  236  (1912),  and  19,  797 
(1913). 


CHAPTER  VIII 

AMMONIACAL  SALT  SOLUTIONS,   ETC. 

From  the  well-known  fact  that  silver  chloride,  a  substance 
which  is  very  slightly  soluble  in  water,  dissolves  freely  in 
ammonia  solution,  we  may  at  once  conclude  that  chemical 
combination  occurs,  and  the  reaction  consists,  presumably, 
in  the  formation  of  a  complex  ion.  Since  all  silver  salts 
show  the  property  of  being  relatively  much  more  soluble 
in  ammonia  than  in  water,  whilst  this  is  not  the  case  with 
all  chlorides,  it  appears  that  the  complex  ion  is  formed  by 
the  combination  of  the  silver  ion  with  ammonia.  This  is 
further  supported  by  the  fact  that  the  silver  ions  as  such 
disappear  during  the  reaction,  while  the  anion  (single  ion) 
does  not. 

During  the  last  fifteen  years  the  constitution  of  silver- 
ammonia  solutions  has  been  the  subject  of  much  study 
which  has  yielded  interesting  and  remarkable  results. 

Bodlander  (Zeit.  phys.  Chem.,  9,  730  (1892))  obtained  and 
analysed  unstable  crystals  from  a  solution  of  silver  chloride 
in  ammonia.  Their  composition  corresponded  to  the  formula 
2AgCl,3NH3.  He  further  determined  the  solubility  of 
silver  chloride  in  solutions  of  ammonia  of  various  strengths, 
and  found  that  the  solubility  rose  rapidly  as  the  concentra- 
tion of  ammonia  was  increased  until  the  latter  reached  a 
value  of  about  5  N.,  when  the  solubility  of  silver  chloride 
became  nearly  constant.  This  concentration  of  ammonia 
(5  N.)  is  also  that  at  which  it  becomes  possible  to  obtain  the 
crystalline  compound. 

Later  (Zeit.  phys.  Chem.,  39,  597  (1902))  Bodlander  and 
Fittig  studied  the  matter  further,  with  very  curious  results. 

73 


74  COMPLEX   IONS 

These  will  be  referred  to  after  we  have  considered  the  work 
of  some  other  observers. 

Keychler  {Bull  de  la  Soc.  Chim.  de  Paris,  13,  386  (1895)) 
found  that  addition  of  ammonia  to  solutions  of  silver  nitrate, 
silver  acetate,  silver  sulphate,  and  silver  nitrite  had  no  effect 
upon  the  freezing  point  until  two  molecules  of  ammonia  had 
been  added  for  each  atom  of  silver  present.  Further  addition 
of  ammonia  caused  a  normal  depression. 

Konowalaw  (Chem.  Zentralblatt,  1898,  II,  659)  measured 
the  pressure  of  ammonia  over  solutions  to  which  successive 
quantities  of  silver  nitrate  were  added,  and  found  that  the 
pressure  was  diminished  to  the  extent  that  would  correspond 
to  the  removal  of  two  molecules  of  ammonia  from  the 
solution  for  each  molecule  of  silver  nitrate  added. 

Dawson  and  McCrae  (Zeit.  anorg.  Chem.,  26,  94  (1901)) 
measured  the  distribution  coefficient  of  ammonia  between 
chloroform  and  water,  and  found  that  on  adding  silver 
chloride  to  the  water  about  1J  molecules  of  ammonia 
disappeared  for  each  molecule  of  silver  chloride  added. 

Gaus  (Zeit.  anorg.  Chem.,  25,  236  (1900))  in  the  course  of 
an  investigation  of  the  effect  of  a  number  of  salts  on  the 
pressure  of  ammonia  over  ammonia  solutions,  found  that  in 
a  l'O  N".  ammonia  solution  saturated  with  silver  chloride 
(0*0491  N".  with  respect  to  AgCl)  the  pressure  was  reduced 
to  an  extent  corresponding  to  the  removal  of  two  molecules 
of  ammonia  for  each  atom  of  silver  present,  calculating 
according  to  Henry's  law,  i.e.  that  the  ammonia  pressure 
was  proportional  to  the  concentration ;  and  he  had  already 
shown  by  preliminary  experiments  that  ammonia  solutions 
obey  Henry's  law  very  closely. 

Bodlander  and  Fittig  (loc.  cit.)  now  made  an  exhaustive 
study  of  the  subject,  which  we  shall  describe  shortly. 

"We  may  express  the  formation  of  the  complex  by  means 
of  the  scheme 

[AgCl]«[NH8]»  =  K[(AgCl),„(NH3)„] 

which  is  the  equation  determining  the  equilibrium  between 


AMMONIACAL  SALT   SOLUTIONS,  ETC.        75 

undissociated  silver  chloride  and  an  undissociated  complex 
salt.  Thus,  if  we  work  in  solutions  saturated  with  respect 
to  silver  chloride, 

[AgCl]m  =  const, 
and  we  obtain 

[NH8]»  -  K1[(AgCl)w(NH3)n]  =  K*D 

where  Ki  is  a  constant  and  D  is  the  concentration  of  the 
undissociated  complex  salt  From  previous  knowledge  of  the 
behaviour  of  complex  silver  solutions  we  may  assume  that 
the  complex  salt  dissociates  into  a  complex  kation  con- 
taining m  atoms  of  silver,  and  m  chlorine  ions  according 
to  the  scheme 

(AgCl)m(NH3)n^  Agw(NH8)„  +  mCY 

the  kation  having  m  positive  charges.     Thus 

D  =  [(AgCl)m(NH3)n]  =  &[Agm(NH3)J[Cl']- 

If  the  degree  of  dissociation  of  the  complex  salt  be  a,  and  its 
total  concentration  Db 

D  =  (1  -  «)D! 

and  D  =  kiaD^aD^  =  k(aD{)m  +  1 

Also         [NH3]^  =  KxD  =  Ki&CaDi)™  + 1  =  ^(aDx)"^ 1 

Hence        [NH3]  =  ^hx .  (aDif^1 

[Note. — The  original  paper  contains  a  very  confusing  slip,  the 
symbol  D  being  used  throughout  for  both  the  concentration  of  the 
undissociated  complex  salt  and  for  the  total  complex  concentration 
without  remark.  Thus  the  calculation  in  the  paper  appears  to  contain 
an  error.  The  above  expression  is  applied  to  the  experimental  results, 
however,  using  the  total  complex  concentration  in  place  of  the 
quantity  we  have  called  Dl9  which,  as  we  have  seen,  is  correct.] 

The  method  followed  consisted  in  determining  the  solu- 
bility of  silver  chloride  in  various  solutions  of  ammonia, 
choosing  ratios  of  the  values  of  n  and  m  +  1,  and  discover- 
ing the  correct  ratio  by  trial.     Only  the  ratio  can  be 


76 


COMPLEX   IONS 


found  in  this  way,  for  clearly  a  series  of  values  of  m  and  n 
will  fit  the  equation 

[NH8]  =  yh .  (aVj^r1 

for  any  value  of  the  ratio.  Thus  m  and  n  cannot  be  deter- 
mined separately  by  this  method. 

As  the  balance  of  evidence  by  previous  observers 
(Eeychler,  Konowalaw  and  Gaus  as  against  Dawson  and 
McCrae)  favoured  the  formula  AgCl,2NH3,  the  values  n  =  2, 
m  =  1  were  tried  first,  and  a  was  taken  as  the  degree  of 
dissociation  of  a  binary  salt,  values  of  a  being  chosen  corre- 
sponding to  those  for  the  alkali  chlorides.  The  concentra- 
tion of  free  ammonia  was  calculated  on  the  assumption  that 
two  molecules  of  ammonia  combined  with  one  molecule  of 
silver  chloride,  in  accordance  with  the  above  values  of  m 
and  n. 

For  this  ratio  of  m  and  n  we  have 

The  solubility  of  silver  chloride  in  ammonia  solutions  was 
determined  at  25°  with  the  following  results  : — 


Table  A. 


1000  grams  of  water  contain 

V*i 

mote. 

Cone,  free 
NH3. 

Active  mass 

of  NH3 

a. 

a'. 

=  A. 

A 

A 

NH3. 

AgClrrDL 

~Dia- 

—  Dia" 

0-0942 

0-004592 

0-0850 

0-0852 

0-95 

0-95 

19-55 

19-55 

0-10065 

0-005164 

0-0903 

0-0906 

0-95 

0-95 

18-47 

18-47 

0-1033 

0-005343 

00926 

0-0929 

0-95 

0-95 

18-31 

18-31 

0-2084 

001137 

0-1857 

0-1868 

0-94 

0-91 

17-56 

18-05 

0-2947 

0-01588 

0-2629 

0-2653 

0-93 

0-88 

18-04 

18-98 

0-4881 

0-02588 

0-4364 

0-4427 

0-91 

0-85 

18-80 

20-12 

0-7522 

0-04758 

0-6570 

0-6714 

0-89 

0-80 

15-85 

17-64 

0-9663 

0-06117 

0-8440 

0-8675 

0-87 

— 

16-23 

— 

1-9004 

0-13616 

1-6281 

1-7150 

0-84 

— 

14-95 

— 

2-8393 

0-2254 

2-3885 

2-5767 

0-82 

— 

14-02 

— 

3-7574 

0-3438 

3-0698 

3-3808 

0-80 

— 

12-36 

— 

4-6918 

0-4680 

3-7558 

4-2212 

0-78 

— 

11-57 

— 

AMMONIACAL  SALT   SOLUTIONS,  ETC.        77 

The  active  mass  of  ammonia  (A)  was  taken  as  being  pro- 
portional to  its  gaseous  pressure.  The  relation  between  the 
gaseous  pressure  (p)  and  the  number  of  gram  molecules  of 
ammonia  per  1000  grams  of  water  (n)  was  determined  by 
Gaus  (loc.  cit.)}  who  found  that  it  could  be  expressed  by  the 
equation 

2  =  12-59(1  +  0-0337i) 

Thus  the  active  mass,  A,  is  given  by 

A  =7i(l  +0-033t0 

Although  the  constant  shows  a  small  progressive  change  in 
the  very  strong  solutions,  it  is  clear  from  the  results  that 

=  1.     Other  ratios   were    tried,    but    the    constant 

n 

changed  very  rapidly.     The  calculations  were   carried  out 

with  values  of  a  for  a  binary  salt,  but  actually  the  value  1 

for  the  ratio  would  also  correspond  to  the  salt  2AgCl,3NH3, 

and  generally  to  salts  of  the  type  (AgCl)m(NH3)m  + 1#     If 

such    salts    were   formed,  however,    they    would  probably 

dissociate    to   a   smaller   extent.      For   example,    the    salt 

2AgCl,3NH3  would  probably  dissociate  to  the  same  extent 

as  other  ternary  electrolytes,  such  as  zinc  chloride.     It  is 

therefore  probable  on  these  grounds  that  the  salt  formed  has 

the  formula  AgCl,2NH3;    and  as  subsequent  experiments 

showed  that  the  formula  2AgCl,3NH3  was  not  possible,  the 

calculations  were  not  carried  further. 

Another  method  was  now  applied,  by  means  of  which  it 

was  shown  that  the  complex  salt  has  not  the  constitution 

expressed  by  the  formula  2AgCl,3NH3.    If  the  salt  has  the 

formula  AgCl,2NH3,  it  will  form  the  kation  Ag(NH3)2*,  and 

this  in  turn  will  dissociate  according  to  the  scheme 

Ag(NH3)2-^Ag--f  2NH3 

This  dissociation  occurs  to  a  very  minute  extent,  so  that  we 
may  write 

[Ag(NH3)2-]  m  «D, 
Hence  k2Dia  =  [Ag-][NH3]2 


78 


COMPLEX   IONS 


Now,    in    solutions    saturated    with    silver    chloride,    the 
solubility  product  [Ag'JfCl']  is  constant,  therefore 

K2aDi  =     ™,-j 

Similarly,  if  the  complex  salt  had  the  formula  2AgCl, 
3NH3,  we  should  have 

lv3aJJi  —     rQT/=j"a" 

Thus  by  measuring  the  solubility  of  silver  chloride  in 
solutions  of  ammonia  containing  various  amounts  of  chlorine 
ions  we  can  distinguish  between  the  two  formulae.  Table  B 
shows  the  results  of  such  a  series  of  determinations. 


Table  B. 


1000  grams  of  water  contain  mols. 

Active  mass 

of  ammonia 

a. 

VK2. 

NH3. 

AgCl. 

KCl. 

A. 

Ai. 

*/K3. 

0-7522 
0-7477 
0-7458 
0-7497 

0-04875 
004392 
0-03869 
0-03330 

0-0 

0-0102 
0-0255 
0-0511 

0-6716 
0-6740 
0-6833 
0-6990 

0-6978 
0-6981 
0-7036 
0-7175 

0-89 
0-88 
0-87 
0-86 

15-87 
15-73 
15-78 
15-71 

66-7 
63-3 

58-4 
49-4 

As  before,  A  is  the  active  mass  of  ammonia,  calculated  on 
the  assumption  that  two  molecules  of  ammonia  combine 
with  one  molecule  of  silver  chloride.  A!  is  the  active  mass 
of  ammonia,  calculated  on  the  assumption  that  three  mole- 
cules of  ammonia  combine  with  two  molecules  of  silver 
chloride,  in  accordance  with  the  second  scheme.  a  is 
Kohlrausch's  value  for  the  degree  of  dissociation  if  all  the 
chlorine  present  were  in  the  form  KCl.  Thus  [CI']  is  given 
in  the  first  case  by 

[CI']  =  afpi  +  Ckci) 

where  Ckci  =  concentration  of  KCl  added,  and  in  the  second 
case  by 

[CI']  =  2a  .  J  +  aCKci 


AMMONIACAL   SALT   SOLUTIONS,   ETC.        79 

i.e.  it  has  the  same  value  in  the  two  cases.  In  the  second 
case  a  would  probably  have  the  value  for  a  ternary  electro- 
lyte instead  of  that  for  a  binary  one,  but  addition  of  small 
quantities  of  potassium  chloride  would  not  alter  its  value  in 
a  manner  very  different  from  that  for  a  binary  electrolyte. 
These  results,  therefore,  show  beyond  doubt  that  the  complex 
salt  is  not  that  represented  by  the  formula  2AgCl,3NH3,  and 
that  it  is  to  be  represented  by  the  formula  raAgCl,wNH3, 
where  n  =  2m.  Since  we  have  proved  that  n  =  m  +  1,  it 
follows  that  m  must  be  equal  to  1  and  n  must  be  equal  to  2. 
An  inspection  of  the  calculations  in  the  two  cases — with  and 
without  addition  of  potassium  chloride — shows  that  K2  in 
Table  B  is  the  same  constant  as  hi  in  Table  A.  The  experi- 
ments show  that  it  has  the  same  value  in  the  two  cases. 

Similar  measurements  were  next  made  with  addition  of 
silver  nitrate  instead  of  potassium  chloride.  If  the  complex 
formation  is  confined  exclusively  to  the  silver  and  ammonia, 
the  same  complex  kation  should  be  formed  when  any  other 
silver  salt  is  present.  If  the  kation  be  Ag(NH3)2*,  we  have, 
as  before, 

^[Ag(NH3)2-]  =  [Ag-][NHJ« 

In  presence  of  solid  silver  chloride, 

[Ag-][C1']  =  const. 

and  thus  K2[Ag(NH3)2«]  -  2^ 

Since  the  chlorine  ions  are  practically  all  produced  by  the 
dissociation  of  the   complex   salt — the   solubility  of  silver 
chloride  in  water  being  negligibly  small  compared  with  its 
solubility  in  these  solutions — we  may  put 
[CI']  =  Dia 

Di,  as  before,  being  equal  to  the  total  concentration  of  silver 
chloride  dissolved.  Also,  calling  the  total  silver  concentra- 
tion c,  we  have 

[Ag(NH3)2-]  =  ac 

a  being  taken  without  considerable  error  as  the  degree  of 


80 


COMPLEX   IONS 


dissociation  of  a  salt  of  concentration  c :  that  is,  the  complex 
chloride  and  the  complex  nitrate  being  treated  as  a  single 
salt.     Thus  we  get 

K   -     A2 

from  which  it  is  obvious  that  addition  of  silver  nitrate  should 
cause  a  depression  in  the  solubility  of  silver  chloride  in 
ammonia  in  a  somewhat  similar  manner  to  potassium  chloride. 
Accordingly,  the  solubility  of  silver  chloride  was  deter- 
mined in  various  solutions  of  ammonia  and  silver  nitrate, 
ammonia  being  in  excess.  In  calculating  the  concentration 
of  free  ammonia  we  must  remember  that  silver  chloride  and 
silver  nitrate  each  combines  with  two  molecules  of  ammonia. 
The  results  are  shown  in  Table  C,  and  show  excellent  agree- 
ment with  the  theory. 


TA.BLE   C. 


1000  grams  of  water  contain  mols. 

A 

a. 

VK2. 

NH3. 

AgCl. 

AgN03. 

0-7522 
0-7517 
0-7503 
0-7550 

0-04758 
0-04173 
003503 
002751 

00 

001021 
0-02556 
005129 

0-6715 
0-6617 
0-6423 
0-6093 

0-89 
0-88 
0-87 
0-87 

15-87 
16-14 
16-02 
15-45 

As  a  further  check  upon  the  conclusions  drawn  we  may 
proceed  to  calculate  the  solubility  of  any  other  silver  salt, 
such  as  the  bromide,  in  ammonia  solutions  if  its  solubility  in 
water  is  known ;  or  conversely,  if  we  know  its  solubility  in 
ammonia  solutions  we  may  calculate  its  solubility  in  water 
in  terms  of  the  solubility  of  silver  chloride. 

Considering  the  case  of  silver  chloride  and  silver  bromide, 
for  each  salt 

;.    _  [Ag-][NH3]» 
"2      [Ag(NH3)2-] 


AMMONIACAL   SALT   SOLUTIONS,  ETC. 
For  the  two  salts  we  have  further,  respectively, 

[Ag']  = 


81 


I^AgCl 


and 


[Ag"]  = 


[CI'] 

LAgBr 

[Br'] 


where  LAgci  and  LA6Br  are  the  soluhility  products. 
Further, 

[CI']  =  [Ag(NH3)2-]ABC1 

and 

[Br']  =  [Ag(NH3)2-]AglJr 

in   the  two  solutions  in   ammonia,  when  no  other  salt  is 

present. 

Thus 


k<2.  — 


'AgCl 


[NH3]2 


'AgBr 


[NH3]! 


Now 
so  that 

or 

Now, 

and 

Hence 


[Ag(NH3)2-]2Agci       [Ag(NH3)2-]2AgBr 
[Ag(NH3)2-]  =  aT>± 

,    _  LAgci[NH3]2  _  LAgBr[NH3]^ 

2  (aDx^gci        '     («Di)2AgBr 

nc   =  v/LAgci[NH3]  _  VLAgBr[NH3] 

2  (aDl)AgCl  (aDl)AgBr 


[NIL 


(aD1)Agci      (aDi^gd 
[NH3]    _        A 


=  V^i     (Table  A). 
=  ^/k±     (Table  D). 


(aD^gBr        (aD1)AgBr 

V'IJAgCl\/^lAgCl  =  -\/LAgBr\/^lAgBr 
\/    AgCl  _  V^lAgBr 


V^AgBr        V^lAgCl 


(A). 


or 


V^AgB,  =  VLAgOl  -^7^7      (B)- 


82 


COMPLEX   IONS 


Table  D  shows  the  values  of  \/^iAgBr  obtained  as  in  the  case 
of  silver  chloride.     The  mean  value  is  322*5. 

Table  D. 


1000  grams  water  contained  mols. 

A. 

A 

^1  =  D7a' 

NH3. 

AgBr. 

01932 

0-00060 

01933 

0-99 

325-4 

0-3849 

0  00120 

0-3874 

0-98 

329-3 

0-5741 

000179 

0-5813 

0-97 

334-9 

0-7573 

000223 

0-7716 

0-96 

360-4 

1-965 

000692 

2-0780 

0-94 

319-6 

3-024 

001163 

3-301 

0-93 

307-7 

5-244 

0-02443 

6-093 

0-91 

280-4 

Mean  =  322-5 


Bodlander  and  Fittisr  took  as  the  weighted  mean  of  the 


values  of  &iAgci  in  Table  A  the  value  18  '46. 

18-46 


This  gives 


\/LAgBr  =  \/^AgCl 


3225 


Now,  \/LAgBr  and  V^Agci  are  the  solubilities  of  silver 
chloride  and  bromide  respectively  in  water,  since  the 
dissociation  of  these  salts  is  practically  complete. 

Goodwin  (Zeit.  phys.  Chem.,  13,  645  (1894))  measured 
the  potential  of  cells  of  the  type 

Ag|K01  sol.  sat.  with  AgCL|AgN03|Ag 

and  was  thus  able  to  calculate  the  solubility  product 
[Ag-][CL'].  He  found  ^/LAgd  =  T25  X  10 ~5  gram  molecule 
per  litre  at  25°.     Using  this  value,  we  find 

V^AgBr  =  7*15  X  10  "7  gram  mols.  per  litre  (Equation  B) 
From  potential  measurements  Goodwin  found 

V^AgBr  =  6*6  x  10  ~7  gram  mols.  per  litre 

Kohlrausch  and  Dolezalek  (Sitzungsber.  der  Berl.  Akad.  d. 
Wiss.,  1901,  101)  found  the  solubility  of  silver  bromide  at 
25°  to  be  71  X  10  "7  gram  mols.  per  litre. 


AMMONIACAL   SALT  SOLUTIONS,  ETC.        83 

Thiel  (Diss.  Giessen,  1900)  found  the  solubilities  at  25° 
to  be  1-41  X  10~5  and  8'1  X  10"7  gram  mols.  per  litre, 
respectively,  giving  the  ratio  v^Agci/VkAgBr  =  17*4  :  1. 
The  ratio  calculated  from  the  values  of  &lAgci  and  &iAgBr  is 
17*5  :  1  (Equation  A). 

Thus  the  theoretical  treatment  of  the  equilibria  which  was 
applied  to  the  case  of  silver  chloride  is  fully  borne  out  in 
the  case  of  silver  bromide. 

Similarly  we  can  now  calculate  the  solubility  in 
ammonia  solutions  of  any  silver  salt  whose  solubility  in  water 
is  known.  For  example,  Goodwin  found  that  the  solubility  of 
silver  iodide  in  water  at  25°  was  0*97  X  10  "8  gram  mol.  per 
litre.     Now 

A/LAgCl 

1-25  x  10-5 


#lAgI   =  — Tf V  ^lAgCl 


0*97  X  lO"8 


X  18-46  =  24,000 


Hence  q  ,  ....       P^  j  . -  =  24,000 

Solubility  ol  Agl  in  ammonia 

or  a  litre  of  normal  ammonia  solution  would  dissolve  24000 
gram  molecule,  or  0*0141  (more  exactly)  gram  of  silver 
iodide. 

Bodlander  and  Fittig  also  examined  solutions  of  silver 
chloride  and  silver  nitrate  in  ammonia  by  the  potential 
method,  and  the  results  showed  that  one  silver  ion  combines 
with  two  molecules  of  ammonia,  in  agreement  with  the 
foregoing  results.     The  cells  measured  were  of  the  type 

Ag|Complex  sol.  I|Complex  sol.  II|Ag 

The  liquid  potential  was  not  taken  into  account. 

It  is  interesting  to  compare  the  values  of  the  dissociation 
constant 

[Ag-][NH3]2 
^  ~  [Ag(NH3)2-] 

obtained  by  the  solubility  and  potential  methods. 


84  COMPLEX   IONS 

In  the  case  of  the  solubility  measurements  we  have 


and  k2  — 


LAgC,[NH3]^ 
(«Dr)« 

Thus  Jc2  =  L^ci  •  A;iAgci 

Taking  Thiel's  values  for  LAgci  and  LAgBr  (1'41  X  10  "5)2  and 
(8*1  x  10 "7)2  respectively,  we  obtain 

k2  =  677  =  10"8 
and  k2  =  6*82  =  10"8 

from  the  results  with  silver  chloride  and  silver  bromide — a 
truly  excellent  agreement. 

In  the  case  of  the  potential  measurements,  the  E.M.F.  of 
the  cell 

Ag|0'025  N.  AgN03  -f  1-0  N.  NH3|0-0093  N.  AgN03|Ag 

was  03879  volt.  Neglecting  the  liquid  potential,  we  find 
for  the  concentration  of  free  silver  ions  in  the  ammoniacal 
solution,  the  value  1*793  X  10 "9  gram  ion  per  litre.  In  the 
equation 

k    _[Ag-][NH3]2 

^      [Ag(NH3)2-] 

[NH3]  =  1*022  and  [Ag(NH3)2-]  =  0025  x  0'95,  taking 
0-95  as  the  degree  of  dissociation  of  the  complex  salt 
Ag(NH3)2N03.     Hence 

h2  =  7-88  x  10"8^ 

in  very  satisfactory  agreement  with  the  values  found  from 
the  solubility  measurements. 

Bodlander  and  Fittig  thus  accumulated  a  very  strong  mass 
of  evidence  for  the  existence  in  solution  of  the  complex  ion 
Ag(NH3)2'.  On  the  other  hand,  the  only  complex  salt  which 
Bodlander  was  able  to  obtain  in  a  solid  form  from  the  silver 
chloride  solution  had  the  composition  2AgCl,3NH3.  This  is 
also  the  compound  formed  when  gaseous  ammonia  reacts 
with  dry  silver  chloride,  within  wide  limits  of  pressure.  How 
are  we  to  explain  the  anomaly  ? 


AMMONIACAL   SALT   SOLUTIONS,  ETC.        85 

Many  solid  silver  salts  are  known  which  do  contain  two 
molecules  of  ammonia  to  each  silver  atom,  such  as  AgI,2NH3 ; 
AgC103,2NH3;  AgBr03,2NH3;  Ag2S04,4NH3;  Ag2S207, 
4NH3 ;  Ag2Se04,4NH3 ;  Ag2Cr04,4NH3 ;  AgN03,2NH3  ; 
AgN02,2NH3;  Ag4As205,8NH3 ;  AgC2H302,2NH3 ;  Ag2C204, 
4NH3;  Ag3C6H507,6NH3  (citrate);  AgC6H5C02,2NH3  ; 
AgC6H2(N02)30,2NH3.  In  addition,  however,  the  follow- 
ing salts  containing  ammonia  are  known,  and  no  indication 
has  been  obtained  of  their  existence  in  solution :  2AgCl, 
3NH3;  2AgBr,3NH3;  AgBr,NH3 ;  AgI,NH3;  2AgI,NH3; 
AgN03,NH3;  AgN02,NH3;  Ag3C3N303,NH3 ;  AgCNS,NH3. 

Some  salts  are  also  known  which  contain  more  than 
two  molecules  of  ammonia  to  one  atom  of  silver,  such  as 
AgCl,3NH3;  AgBr,3NH3;  AgN02,3NH3;  AgN03,3NH3 
(see  Keychler,  Les  Derives  ammonicaux  des  sels  d'argent, 
Bruxelles,  1884;  Joannis  and  Crozier,  Comptes  Bendus,  118, 
1149  (1894)).  Thus  it  would  appear  that  the  existence  of  a 
solid  salt  affords  little  evidence  as  to  the  state  of  affairs  in  a 
solution  from  which  it  crystallises.  This  is  fully  borne  out 
by  theoretical  considerations.  The  point  was  discussed  in  a 
very  illuminating  manner  by  Abegg  and  Hamburger  (Zeit. 
anorg.  Chem.,  50,  403),  who  point  out  that  the  deposit  from  a 
solution  must  always  consist  of  the  substance  whose  satura- 
tion concentration  is  first  reached  at  the  temperature  of 
the  experiment.  The  question  as  to  what  substance  will 
crystallise  from  a  complex  solution  is  thus  purely  one  of 
solubilities  and  the  equilibria  existing  in  the  solution.  Thus 
a  compound  of  small  solubility  may  crystallise  from  a 
solution  in  which  it  is  present  only  to  a  minute  extent  in 
equilibrium  with  large  quantities  of  other  substances.  It 
must  be  noticed  that  the  solubility  we  refer  to  here  means 
the  concentration  in  the  solution  of  the  molecules  which 
form  the  solid,  and  not  the  apparent  solubility  we  should 
find  if  we  shook  up  the  solid  with  water  until  no  more 
would  dissolve.  In  the  latter  case  we  should  obtain  a 
solution,  saturated  indeed  with  the  molecules  of  which  the 
solid  was  composed,  but  containing  besides  other  products 


86  COMPLEX   IONS 

formed  by  the  partial  dissociation  of  these  molecules  and 
the  subsequent  partial  recombination  of  the  products  in 
different  proportions.  The  compound  in  question,  2AgCl, 
3NH3,  can  only  be  obtained  from  strong  ammonia  solutions, 
so  that  if  we  shook  it  up  with  water  silver  chloride  would 
separate  until  the  ammonia  concentration  was  great  enough 
to  hold  the  remaining  silver  chloride  in  solution  in  the  form 
AgCl,2NH8. 

There  is  thus  no  real  anomaly  in  the  case,  and  the 
behaviour  might  be  expected  under  suitable  circumstances. 

Abegg  and  Cox  (Zeit.  phys.  Chem.}  46,  11  (1903))  made 
use  of  Bodlander  and  Fittig's  results  in  order  to  determine 
the  solubility  of  silver  thiocyanate.     In  this  case  we  have 

[Ag(NH8y] 

Since  silver  thiocyanate  is  a  very  slightly  soluble  salt 
we  may  put 

[Ag(NH3y]  =  pros']  =  c 

where  c  is  the  solubility  of  silver  thiocyanate  in  a  solution  of 
ammonia.     Thus,  in  such  a  solution 

[Ag'INH,]"  =  ho 
and  [Ag-][NCS']  =  L 

Hence  \/L  =  [NHl  ■  V^a 

In  this  way  the  solubility  of  silver  thiocyanate  in  water 

was   determined   by  measuring   its   solubility  in   ammonia 

solutions.      The   original   paper   contains   many   numerical 

errors,  so  the  results  in  the  following  table  have  all  been 

recalculated,    taking    the    experimental    results    as    being 

correctly  printed,  saving  in  one  case  to  which  attention  is 

102c 
drawn.     The  mean  value  of  f^^r^  is  almost  identical  with 

[NH*] 

that  used  by  the  authors  in  calculating  the  solubility  of 
silver  thiocyanate. 


AMMONIACAL   SALT   SOLUTIONS,  ETC.        87 


Ammonia. 

c. 

100  cu 

Free  NH3. 

Active  mass  > 
ofNH3. 

103C 

[NH3]  * 

0-2761 
0-4435 
0-5865 
1-3247 

0-001518 
0-002139 
0-00295 
0-00720 

95 
95 
95 
94 3 

0-2731 2 
0-4392 
0-5806 
1-3103  2 

0-27562 
0-4455  2 
0-5917  2 
1-367  2 

5-232 
4-56  2 
4-73  2 
4-952 

Mean  =  4-87 


Thus  fsrs"i  =  4-87  x  10 

[NH3] 


The  mean  of  the  values  given 
in  the  original  paper  was  4*5  x  10~3. 


Taking  ^jy  =  4*87  X  10  "3,  we  find 

VL  =  4-87  x  KTV6-8  x  10"8  =  1*27  x  10"6 

The  value  found  in  the  original  paper  was  1'25  x  10 "6, 
so  that  the  errors  have  probably  not  been  due  to  mistakes  in 
calculation.  An  examination  on  similar  lines  of  solutions 
of  silver  iodide  and  potassium  iodide,  silver  thiocyanate  and 
potassium  thiocyanate,  and  of  silver  cyanide  and  potassium 
cyanide,  was  made  by  Bodlander  and  Eberlein  (Zeii.  anorg. 
Chem.,  39,  197  (1904)),  and  of  silver  cyanide  in  ammonia  by 
Lucas  (Zeit.  anorg.  Chem.,  41,  193  (1904)). 

The  last-mentioned  paper  contains  an  interesting  point 
which  we  may  briefly  refer  to.  Lucas  found  that  his  experi- 
mental values  for  the  solubility  of  silver  cyanide  in  ammonia 
could  only  be  explained  by  supposing  that  the  complex  salt 
which  yielded  the  ions  Ag(NH3)2*  and  Ag(CN)2'  was  only 
slightly  dissociated.  The  degrees  of  dissociation  were 
calculated  for  a  number  of  solutions  of  ammonia  saturated 
with  silver   cyanide,  which   would   bring  his   values    into 

1  Calculated  by  means  of  Gaus'  formula  (loc.  cit.). 

2  Differs  from  the  value  in  original  paper. 

3  Given  as  97  in  original  paper. 


88  COMPLEX  IONS 

accord  with  the  results  of  Bodlander  and  Fittig,  and  the 
dissociation  constants 

[Ag(NH3)2-][Ag(0N)2'] 
*»-     [Ag(NH3)2Ag(CN)2] 

_  [Ag(NH3)2-][Ag(CN)2'] 
2  ~  [AgCNNH3]2 

were  calculated,  corresponding  to  the  schemes 

Ag(NH3)2Ag(CN)2^Ag(NH3)2-  +  Ag(CN)2' 

and  2  AgCNNH3  ^  Ag(NH3)2-  +  Ag(CN)2' 

respectively. 

It  was  found  that  K2  showed  satisfactory  constancy,  while 
Ki  was  not  at  all  constant,  indicating  that  the  undissociated 
complex  salt  has  the  formula  AgCNNH3,  and  dissociates 
according  to  the  second  of  the  above  schemes.  Further 
support  was  given  to  this  conclusion  by  the  fact  that  the 
degree  of  dissociation  calculated  by  means  of  Bodlander  and 
Fittig's  results  was  almost  independent  of  the  concentration. 
This  is  only  possible  in  the  case  of  salts  which  dissociate  in 
such  a  way  that  the  dissociation  does  not  affect  the  osmotic 
pressure  of  the  solution — a  very  unusual  condition,  which  is, 
however,  fulfilled  by  the  reaction 

2AgCNNH3  ^  Ag(NH3)2-  +  Ag(CN)2' 

This  conclusion  completely  accounts  for  the  large  mass  of 
experimental  results  obtained  by  Lucas,  and  harmonises  them 
perfectly  with  the  observations  of  Bodlander  and  Fittig. 

An  interesting  general  study  of  the  effects  of  a  large 
number  of  salts  upon  the  ammonia  pressures  of  ammonia 
solutions  was  made  by  Gaus  (Zeit.  anorg.  Chem.,  25,  236 
(1900)).     The  method  adopted  was  as  follows  : — 

Electrolytic  gas,  generated  from  a  cell  consisting  of 
nickel  electrodes  immersed  in  caustic  soda  solution,  was 
passed  through  two  large  wash-bottles  containing  the 
ammonia-salt  solution,  and  then  through  a  conductivity 
vessel  containing  a  small  quantity  of  dilute  (0'01-0-025  N.) 


AMMONIACAL  SALT   SOLUTIONS,  ETC.         89 

hydrochloric  acid.  The  whole  apparatus  was  placed  in  a 
thermostat. 

The  volume  of  electrolytic  gas  used  was  calculated  from 
the  weight  of  copper  deposited  in  a  voltameter  which  was 
switched  into  the  circuit  at  the  instant  that  the  gas  stream 
was  diverted  into  the  conductivity  vessel.  Thus  by  observing 
the  diminution  in  the  conductivity  of  the  hydrochloric  acid 
and  the  weight  of  copper  deposited  in  the  voltameter,  the 
pressure  of  ammonia  in  the  gas  issuing  from  the  wash-bottles 
could  be  calculated.  For  details  of  the  apparatus  and  control 
experiments  the  reader  is  referred  to  the  original  paper. 
The  first  experiments  to  determine  the  effect  of  added  salts 
upon  the  ammonia  pressure  were  made  with  salts  having  an 
ion  in  common  with  the  compound  NH4OH,  namely,  caustic 
soda  on  the  one  hand,  and  various  ammonium  salts  on  the 
other. 

A  normal  solution  of  ammonia  which  was  also  04  N. 
with  respect  to  caustic  soda  had  an  ammonia  pressure 
of  14-96  mm.  at  25°,  while  the  pressure  of  TO  N.  ammonia 
solution  alone  is  13*45  mm.  Thus  the  caustic  soda  caused 
an  increase  in  the  ammonia  pressure  of  1*51  mm.,  or  more 
than  10  per  cent.  Gaus  considers  this  increase  much  too 
great  to  be  accounted  for  by  diminution  in  the  dissociation 
of  the  compound  NH4OH,  and  suggests  that  most  of  it  is  due 
to  the  presence  of  a  second  solute,  i.e.  the  caustic  soda 
(see  Bothmund,  Zeit.  phys.  Chem.,  33,  410  (1900)).  It  may 
be  added  that  in  this  case  hydrate  formation  is  likely  to 
play  a  prominent  part,  since  caustic  soda  is  known  to  form 
comparatively  stable  solid  hydrates,  and  is  probably  highly 
hydrated  in  solution  (see  Pickering,  Trans.  Chem.  Soc., 
1895,  890).  This  effect  stands  in  marked  contrast  to  the 
action  of  ammonium  salts,  as  shown  in  the  accompanying 
table. 


90 


COMPLEX    IONS 


Added  salt  cone. 
=  04  N. 


NH4C1       . 

NH4N03  . 
NH4I  .  . 
NH4NCS  . 


/13-151 
11817/ 


/12-92\ 
\12-85J 

/12-83\ 
\12-82/ 


III. 

Mean  value  of  D 


13-34 

13-16 
12-83 
12-82 


IV. 

Pressure  calcu- 
lated for  1-0  N. 
NIL. 


13-54 

13-43 
13-20 
13-18 


Alteration  caused 
by  salt. 


+  009 

-0-02 
-0-25 
-0*27 


D  represents  the  pressure  found  in  millimetres  of  mercury. 
The  solution  was  titrated  at  the  end  of  the  experiment,  so 
as  to  avoid  the  error  caused  by  loss  of  ammonia  during  the 
addition  of  the  salt.  The  amount  of  ammonia  removed  by 
the  gas  during  the  experiment  was  negligible.  The  pressures 
which  would  have  been  produced  by  an  exactly  normal 
solution  of  ammonia  were  calculated  and  are  given  in 
Column  IV. 

Thus  addition  of  ammonium  ions  does  not  cause  an 
increase  in  the  pressure  of  ammonia.  Actually  all  the 
values  must  be  a  little  too  high,  since  the  mass  of  water 
present  per  litre  is  less  than  in  a  1*0  N.  ammonia  solution. 
The  correction,  as  calculated  by  Gaus,  amounts  to  1*2-2*0 
per  cent.  Thus  it  looks  as  if  some  chemical  reaction 
occurs,  either  a  complex  ion  of  the  type  NH4(NH3)'  or 
a  salt  analogous  to  a  hydrated  salt,  in  which  water 
is  replaced  by  ammonia  being  formed.  Gaus  points  out 
that  these  two  views  are  practically  identical,  since 
it  is  certain  that  many  ions  in  solution  are  hydrated, 
and  such  hydrates  fall  within  the  definition  of  complex 
ions. 

A  further  series  of  measurements  with  ammonium  salts 
of   dibasic  acids,    however,  showed   that   in   this   case   the 


AMMONIACAL   SALT   SOLUTIONS,   ETC.         91 

behaviour  is   entirely  different,  as  will  be   seen  from   the 
following  table : — 


Added  salt  0'4  molar. 

D. 

Mean  pressure 
calculated  for 
ION.  NH3. 

Alteration. 

«  l(NH4)aS04      .     . 
^(NH4)2C204     .     . 
!  i(NH4)2C4H406     . 

/14-10\ 
\14-14J 

/13-95\ 
\13-97| 

/13-70\ 
\13-67J 

14-42 
14-27 
13-83 

+  0-97 
+  0-82 
+  0-38 

The  idea  of  attributing  the  increases  of  pressure  caused 
by  di-basic  ammonium  salts  to  hydrolysis  may  be  summarily 
dismissed,  as  calculation  from  the  known  dissociation  con- 
stants shows  that  it  would  be  immeasurably  small.  Also 
the  tartrate,  as  the  salt  of  the  weakest  acid,  should  show 
the  greatest  increase  in  pressure,  whilst  it  actually  shows  the 
smallest. 

The  divergence  in  behaviour  between  the  "mono-  and 
dibasic  ammonium  salts  cannot  be  explained  on  the  grounds 
that  the  concentrations  of  the  ammonium  ions  are  greater  in 
the  case  of  dibasic  salts,  since  the  monobasic  salts  are  much 
more  highly  dissociated  than  the  dibasic  ones. 

Hantzsch  and  Sebaldt  (Zeit.  phys.  Chem.,  30,  258  (1899)) 
made  measurements  of  the  distribution  coefficient  of  ammonia 
between  water  and  chloroform  in  presence  of  ammonium 
chloride  (in  the  water  layer),  and  found  that  increasing  the 
concentration  of  ammonium  chloride  did  not  alter  the 
apparent  distribution  coefficient,  in  approximate  agreement 


1  These  concentrations  are  given  in  the  original  as  0-4  molar  with 
respect  to  the  complete  salt  molecule.  In  the  complete  table  of  the 
results  at  the  end  of  the  paper,  however,  the  formula  is  written 
"  £(NH4)2S04,"  etc.,  and  it  seems  probable  that  these  solutions  were  0-4  N. 
in  common  with  all  the  others  examined,  especially  in  view  of  the 
comparison  drawn  by  Gaus  between  these  solutions  and  those  of  the  mono- 
basic ammonium  salts. 


92  COMPLEX   IONS 

with  Gaus's  results ;  and  they  obtained  a  similar  result  with 
piperidin,  which  is  much  more  dissociated  than  ammoniui 
hydroxide.  On  the  other  hand,  addition  of  caustic  soda 
caused  an  increase  in  the  concentration  of  ammonia  in  the 
chloroform  layer,  also  in  agreement  with  Gaus's  results. 
Unfortunately  no  experiments  were  made  with  dibasic 
ammonium  salts. 

Arrhenius  (Zeit.  phys.  Chem.,  1  (1887))  found  that  addi- 
tion of  monobasic  ammonium  salts  causes  a  considerable 
reduction  in  the  speed  of  saponification  of  ethyl  acetate 
by  ammonia,  while  the  reduction  caused  by  addition  of 
ammonium  sulphate  was  much  smaller.  Parallel  experi- 
ments with  potassium,  sodium  and  barium  salts,  and  the 
corresponding  hydroxides,  showed  an  abnormality  precisely 
similar  to  that  shown  by  ammonium  salts  in  the  ammonia 
pressure  experiments,  the  halides  and  the  nitrate  in  each 
case  reducing  the  speed  of  saponification,  while  the  sulphates 
of  potassium  and  sodium  increased  it — a  fact  for  which  no 
explanation  has  been  offered. 

Subsequent  work  by  Abegg  and  Eiesenfeld  (Zeit.  phys. 
Chem.,  40,  84  (1902))  on  the  effect  of  addition  of  salts  of 
metals  which  do  not  readily  yield  complex  ions  (mainly 
alkali  salts)  to  ammonia  solutions  upon  the  pressure  of  the 
latter  showed  that  the  anion  plays  a  certain  part  in  the 
effect. 

The  divergence  in  behaviour  of  the  mono-  and  di-basic 
ammonium  salts  in  ammonia  solutions  must  be  regarded  as 
a  puzzle. 

Keturning  to  Gaus's  experiments,  the  results  found  by 
him  are  shown  in  the  following  table : — 


AMMONIACAL   SALT   SOLUTIONS,  ETC.         93 


1*0  N.  Ammonia  Solution. 


Added  salt. 

Cone,  "£ 
litre 

AD  mm.  mercury. 

AD 

-f-  cone. 

13*45 

of  added  salt. 

NaOH       .      .     . 

0-4 

+  1-51 

KC1     .     . 

0-4 

+  100 

— 

rtfNH4)2S04 

Bnh&oa 

0-4 

+  0-97 

— 

0-4 

+  0-82 

— 

NaCl    .     . 

0-4 

+  0-79 

— 

1(NH4)2G4H4( 

). 

0-4 

+  0-38 

— 

NH4C1      . 

0-4 

+  0-09 

— 

NH4N03 

0-4 

-0-02 

— 

Bad,  . 

04 

-002 

— 

NH4f  . 

04 

-0-25 

— 

NH4NCS 

0-4 

-0-27 

— 

SrCl2   . 

0-4 

-0-29 

— 

Ca012  . 

0-4 

-0-77 

— 

MgCl,  . 

0-4 

-201 

— 

CuS04 

0-0982 

-5-02 

3-8 

CuS04 

00491 

-2-49 

3-8 

CtfCl  . 

002 

-0-44 

1-6 

AgCl    . 

0-0491 

-1-39 

2-1 

ZnS04. 

001 

-0-44 

3-3 

CdS04 

001 

-052 

3-9 

The  figures  in  the  last  column  show  the  number  of 
ammonia  molecules  removed  by  each  molecule  of  the  added 
salt.  The  results  with  silver  and  copper  thus  agree  well 
with  those  of  other  observers. 

For  an  examination  of  solutions  of  Cu(OH)2,  Ni(OH)2, 
Cd(OH)2,  Zn(OH)2,  and  Ag20  in  ammonia,  see  Bonsdorff 
(Zeit.  anorg.  Chem.,  46,  132  (1904)). 

Similar  experiments  were  made  with  sulphur  dioxide  by 
C.  J.  J.  Fox  (Zeit.  phys.  Ghem.t  41,  458  (1902)).  Fox 
extended  the  use  of  Kothmund's  (he.  eit.)  formula  for  the 
solubility  of  a  substance  in  water  containing  an  indifferent 
salt,  namely 

1      h-l 


n 


L 


=  const. 


where  n  =  salt  concentration, 

k  =  solubility  of  substance  in  water, 

I  =  solubility  of  substance  in  salt  solution. 


94  COMPLEX   IONS 

Now,  if  the  heats  of  solution  of  the  substance  in  water  and 
in  the  salt  solution  respectively  be  q0  and  q,  we  have 
q0  _  d  log  l0 
2T2         dT 

and  q    -dlo%1 

anu  2T2  -      dT 

If  q0  is  n°t  equal  to  q,  the  difference  must  be  the  heat 
effect  of  a  chemical  reaction  between  the  salt  and  th( 
subtance  dissolved.     Calling  this  qh  we  have 

?0  -  2  =  IT—  2T2  =  qi 

that  is,  if  the  ratio  of  the  solubilities  in  water  and  in  th( 
salt  solution  changes  with  temperature,  a  thermochemical 
reaction  must  have  occurred  between  the  two  solutes. 

The  absorption  coefficient  of  sulphur  dioxide  was 
measured  in  solutions  of  twelve  salts  at  25°  and  at  35°,  and 

in  each  case  the  values  of  -  ,-~ — -  showed  a  temperature 

coefficient,  excepting  the  cases  of  the  three  salts,  ammonium 
sulphate,  sodium  sulphate,  and  cadmium  sulphate,  thus 
indicating  a  reaction  between  gas  and  solute. 

The  absorption  coefficient  was  also  measured  at  25°  in 
solutions  of  various  strengths  of  the  following  salts :  KI, 
KNCS,  KBr,  KC1,  KN03,  (NH4)2S04.  In  each  case  the 
measurements  were  carried  out  at  two  pressures  of  sulphur 
dioxide,  namely,  760  mm.  and  77*93  mm.,  the  sulphur 
dioxide  in  the  latter  case  being  diluted  with  carbon  dioxide. 
The  accompanying  table  shows  the  value  of  the  expression 

1      I  -  k 
p.n      l0 

at  25°,  p  being  the  pressure  of  sulphur  dioxide.  The  ex- 
pression has  a  constant  value  for  each  salt,  showing  that  the 
quantity  of  sulphur  dioxide  which  combines  with  the  salt  is 
proportional  to  the  first  power  of  p.  The  change  in  the 
absorption  coefficient  is  also  proportional  to  n,  so  that  in 


AMMONIACAL   SALT   SOLUTIONS,  ETC.         95 


each  case  the  formula  of  the  complex  salt  formed  (if  any) 
must  be 

one  molecule  salt :  one  molecule  sulphur  dioxide. 

The  conductivities  of  solutions  of  many  salts  alone  on 
the  one  hand,  and  saturated  with  sulphur  dioxide  on  the 
other,  were  also  measured.  In  weak  salt  solutions  addition 
of  sulphur  dioxide  caused  an  increase  in  conductivity,  as 
was  to  be  anticipated  from  the  fact  that  sulphurous  acid  is 
formed.  Plotting  the  conductivities  as  ordinates  against 
salt  concentrations  as  abscissse,  however,  we  find  that  the 
conductivity  of  salt  solutions  saturated  with  sulphur  dioxide 
rises  more  slowly  than  that  of  the  salt  solutions  alone,  and 
in  many  cases  the  two  curves  cut  one  another  at  about 
2*0  N.  In  these  cases  a  slow-moving  complex  ion  must 
have  been  formed. 


Salt. 

Pressure  of 
S02. 

Salt  concentration. 

3N. 

2-5  N. 

2-0  K. 

1-5  N. 

ION. 

0-5  N. 

KI  .  .  . 

/760  mm. 
\  77*93  mm. 

0-00476 
0-00464 

0-00480 
000451 

0-00481 
0-00465 

0-00478 
000465 

0-00482 
0-00477 

0-00461 
0-00471 

KNCS  .  . 

/760  mm. 
\77-93mm. 

0-00380 
0-00385 

0-00371 
0-00384 

0-00383 
0-00377 

0-00382 
0-00376 

0-00387 
000379 

0-00387 
000385 

KBr  .  .  . 

/760  mm. 
\  77*93  mm. 

0-00254 
000245 

0-00252 
0-00248 

0-00255 
000252 

0-00245 
000243 

0-00256 
0-00245 

0-00255 
000269 

KC1  .  .  . 

(760  mm. 
\  77 -93  mm. 

0-00127 
0-00135 

000131 
0-00129 

000131 
000135 

000134 
0-00139 

0-00128 
0-00130 

0-00133 
0-00136 

lKN03  .  . 

/760  mm. 
\77-93mm. 

0-00077 
0-000802 

0-000773 
0000801 

0-000761 
0000826 

0-000786 
0000781 

0-000814 
0-000768 

0-000834 
0O00774 

^(NH4)2S04 

/760  mm. 
\77-93mm. 

0-000428 
0-000427 

0000436 
0-000434 

0-000440 
0-000423 

0-000424 
0-000423 

0000426 
0-000422 

0-000474 
0-000427 

Finally  it  was  found  possible  in  several  cases  to  isolate 
solid    compounds    of    sulphur    dioxide    with    salts.      The 

1  The  figures  given  for  these  salts  in  the  original  paper  were  all  (save 
the  first)  10  times  as  great  as  those  recalculated  from  the  experimental 
data.     The  figures  given  are  therefore  all  recalculated. 


96  COMPLEX   IONS 

powdered  solid  salt  was  moistened  with  a  little  water,  and 
a  stream  of  dry  sulphur  dioxide  was  passed  over  the  mixture 
until  it  became  dry.  The  tube  containing  the  solid  was  now 
weighed,  and  warmed  until  all  the  sulphur  dioxide  was 
driven  off.  On  weighing  again,  the  weight  was  found  to  be 
that  of  the  tube  and  the  original  quantity  of  salt.  Thus  the 
amount  of  sulphur  dioxide  absorbed  was  determined.  In 
the  cases  of  KI,  KBr,  KC1,  and  KNCS,  the  weights  of 
sulphur  dioxide  absorbed  were  95,  90,  91,  and  93  per  cent, 
respectively  of  the  quantity  required  for  complete  formation 
of  the  compound  KXS02,  where  X  represents  the  acid 
radical.  Potassium  nitrate  showed  no  absorption  at  all,  so 
that  although  the  compound  KNO3SO2  can  probably  exist, 
it  must  have  a  pressure  of  more  than  760  mm.  of  sulphur 
dioxide  at  the  ordinary  temperature. 

Walden  and  Centnerszwer  (Zeit.  phys.  Chem.,  42,  432 
(1902))  succeeded  in  preparing  and  analysing  the  solid  com- 
pound KI,4S02.  Freezing-point  experiments  appeared  to 
show  the  presence  of  KI,4S02  and  KI(13-16)S02  in 
solution.  The  latter  compound  was  also  separated  in  a 
more  or  less  pure  condition.  Analysis  showed  it  to  contain 
(1)  15-8,  (2)  14-6,  (3)  15*2  molecules  of  sulphur  dioxide  for 
each  molecule  of  potassium  iodide. 


CHAPTEE  IX 

SOME  COBALT  AND  COPPER  SOLUTIONS 

A.  The  Cobalt  and  Cupric  Halides. 

A  solution  of  cobalt  chloride  in  water  has  a  decided  red 
colour,  but  addition  of  certain  chlorides,  such  as  hydrochloric 
acid,  magnesium  chloride  or  calcium  chloride,  causes  the 
colour  to  change  from  red  to  blue. 

If  the  blue  colour  is  due  to  formation  of  a  complex  ion, 
such  as  C0CI3'  or  C0CI4",  we  should  expect  to  find  that  on 
passing  a  current  through  a  cell  having  its  kathode  immersed 
in  the  blue  solution  and  its  anode  in  a  colourless  electrolyte, 
a  blue  colour-boundary  would  move  from  the  kathode  towards 
the  anode. 

The  experiment  was  made  by  Donnan  and  Bassett 
(Trans.  Chem.  80c,  1902,  939).  Two  vessels  were  filled 
with  the  blue  solution  of  cobalt  and  calcium  chlorides 
and  connected  by  a  tube  containing  pure  calcium  chloride 
solution.  On  passing  a  current  through  the  cell  a  blue 
colour-boundary  entered  the  tube  from  the  kathode  end  and 
travelled  towards  the  anode,  while  no  colour  appeared  in  the 
tube  at  the  anode  end. 

On  the  other  hand,  if  the  two  end  vessels  were  filled  with 
red  cobalt  chloride  solution  whilst  the  connecting  tube  con- 
tained a  solution  of  potassium  chloride,  a  pink  layer  entered 
the  tube  from  the  anode  vessel,  and  travelled  towards  the 
kathode,  and  no  colour-boundary  entered  the  tube  from  the 
kathode  vessel. 

Again,  an  alcoholic  solution  of  cobalt  chloride  conducts 
electricity  freely,  while  the  apparent  molecular  weight  of 
the  salt  as  determined  by  the  boiling  point  is  a  little  higher 

97  h 


98  COMPLEX  IONS 

than  the  normal,  viz.  140  instead  of  130.  Donnan  and 
Bassett  pointed  out  that  if  the  salt  ionised  according  to  the 
scheme 

2CoCl2^Co"  +  CoCl4" 
the  solution  would  conduct  electricity  although  the  apparent 
molecular  weight  would  remain  normal.     They  also  quoted 
the  following  evidence  for  the  existence  of  complex  anions 
containing  cobalt : — 

1.  Solubility. 

Sabatier  (Oomptes  Rendus,  107,  42)  showed  that  the 
solubility  of  cobalt  chloride  in  water  is  first  diminished 
and  then  increased  by  continuous  addition  of  hydrochloric 
acid. 

2.  Conductivity. 

Trotsch  {Ann.  der  Physik  und  Chemie,  41,  259  (1890)) 
found  that  the  temperature-coefficient  of  the  conductivity  of 
strong  solutions  of  cobalt  chloride  at  first  increases  with  rise 
in  temperature  and  then  diminishes.  There  is  a  point  of 
inflexion  in  the  conductivity-temperature  curve  between  40° 
and  50°,  beyond  which  the  temperature  coefficient  is  negative. 
Similar  points  of  inflexion  are  shown  by  cupric  chloride  and 
some  sulphates,  while  all  binary  electrolytes  examined,  such 
as  chlorides,  nitrates,  chlorates,  etc.,  of  the  alkali  metals  show 
continually  increasing  temperature-coefficients. 

3.  Transport  Numbers. 

Bein  (Zeit.  phys.  Chem.,  27,  1  (1898))  found  that  the 
transport  number  for  cobalt  in  cobalt  chloride  solutions 
decreases  as  the  concentration  rises.  The  experiments  were 
carried  out  at  different  temperatures,  however,  so  that  this 
evidence  is  of  somewhat  doubtful  value. 

4.  Heat  of  Dilution. 

The  fact  that  the  temperature-coefficient  of  the  con- 
ductivity falls  with  rise  of  temperature  and  ultimately 
becomes  negative  shows  that  the  reaction  which  lowers  the 
conductivity  is  favoured  by  rise  of  temperature  and  is  there- 
fore endothermic.  This  reaction  is  probably  the  formation  of 
complex  ions,  since  simple  electrolytic  dissociation  usually 


SOME  COBALT   AND   COPPER   SQLUTIONS     99 

increases  very  fast  with  rise  of  temperature.  If  this  is  the 
case,  heat  should  be  evolved  on  diluting  the  solution,  owing 
to  the  dissociation  of  the  endothermic  complex  salt.  Experi- 
ment shows  that  this  is  the  case. 

Donnan  and  Bassett  therefore  concluded  that  the  blue 
colour  was  due  to  the  complex  ion  C0CI3'  or  C0CI4" :  C0CI2 
was  probably  blue,  Co**  was  red. 

Biltz  (Zeit.phys.  Chem.,  40, 198  (1902))  showed  that  cobalt 
chloride  and  cupric  chloride  and  bromide  have  unusually  big 
freezing-point  depressions  in  water  solution,  presenting  a 
marked  contrast  to  the  boiling  point  of  cobalt  chloride 
solutions  in  alcohol.  This  would  agree  with  Donnan  and 
Bassett's  theory,  however,  that  complex  formation  is  small  at 
low  temperatures  and  large  at  high  ones. 

Kohlschutter  (Ber.,  37,  1,  1153  (1900))  carried  out 
migration  experiments  with  cupric  chloride  solutions,  and 
concluded  that  there  was  no  doubt  as  to  the  formation  of 
complex  ions  in  them. 

G.  N.  Lewis  (Zeit.  phys.  Chem.,  52,  222,  and  56,  223) 
observed  the  colours  produced  by  adding  cupric  bromide 
to  3  M.  solutions  of  a  large  number  of  salts.  The  colours 
varied  from  blue  to  green  except  in  the  case  of  other 
bromides,  when  brown  solutions  were  formed.  Cupric 
chloride  gave  a  green  colour  in  chloride  solutions,  and  blue 
in  all  others.  Cobalt  chloride  was  red  in  all  solutions  save 
those  of  chlorides,  when  it  had  a  bluish  tint, 

Lewis  concluded  that  the  colour  changes  were  due  to 
change  in  the  degree  of  hydration,  but  the  evidence  for  this 
appears  somewhat  weak.  It  is  significant  that  special 
results  were  produced  in  each  case  by  salts  having  a  common 
ion. 

Benrath  (Zeit.  anorg.  Chem.,  54,  328  (1907))  found  that 
certain  chlorides,  such  as  mercuric,  zinc,  cadmium  and 
stannous  chlorides,  instead  of  producing  a  blue  colour  in 
solutions  of  cobalt  chloride,  hinder  its  production.  Measure- 
ments of  the  boiling  points  of  aqueous  solutions  of  these  salts 
in  presence  of  cobalt  chloride  showed  that  the  rise  was  much 


100  COMPLEX  IONS 

smaller  than  was  to  be  expected  under  ordinary  conditions  of 
dissociation,  and  it  was  therefore  to  be  assumed  that  complex- 
formation  had  occurred.  Experiments  with  barium,  calcium, 
sodium,  magnesium,  aluminium  and  hydrogen  chlorides 
showed  that  with  these  salts  the  rise  in  the  boiling  point 
was  normal.  These  are  the  salts  that  increase  the  blue 
colour.  Donnan  and  Bassett's  theory  was  therefore  called 
into  question. 

Denham  (Zeit  phys.  Chem.,  65,  641)  next  studied  the 
subject  and  measured  the  migration  ratio  in  solutions  of 
cupric  chloride  and  bromide  and  of  cobalt  bromide.  As  the 
concentration  increases,  the  migration  ratio  for  the  kation 
becomes  continually  less.  Unless  very  abnormal  changes  in 
the  degree  of  hydration  are  assumed  to  occur,  this  must 
necessarily  be  due  to  the  formation  of  complex  anions, 
probably  of  the  type  CoCl3'  or  CoCl4".  The  changes  in 
colour  are  approximately  parallel  to  the  changes  in  the 
constitution  of  the  solution  on  this  hypothesis. 

Further,  in  reply  to  Benrath,  it  was  pointed  out  that 
while  addition  of  a  salt  such  as  calcium  or  magnesium 
chloride  will  obviously  cause  a  large  increase  in  the  amount 
of  complex  ions  formed,  addition  of  a  salt  having  a  stronger 
tendency  to  form  complex  ions  or  undissociated  salts,  such  as 
mercuric  or  cadmium  chloride,  will  cause  a  diminution  in  the 
amount  of  cobalt  complex  present. 

This  theory  appears  to  offer  a  fairly  complete  account 
of  the  facts.  At  the  same  time,  the  fact  that  calcium  and 
magnesium  chlorides  show  a  greater  tendency  to  cause  for- 
mation of  the  blue  colour  than  the  alkali  chlorides  seems  to 
indicate  that  the  high  degree  of  hydration  which  these  salts 
probably  possess  in  solution  favours  formation  of  the  com- 
plex ion  containing  cobalt  by  reducing  the  active  mass  of 
water  in  the  solution,  so  that  both  hydrate-  and  complex- 
formation  perhaps  play  a  part  in  the  phenomena. 

Jones  (Zeit.  phys.  Chem.,  74,  358  (1910))  is  of  opinion 
that  the  colour  changes  are  caused  by  change  in  the  degree 
of  hydration. 


SOME   COBALT   AND   COPPER   SOLUTION'S     101 

B.  Fehling's  Solution,  etc. 

Another  class  of  solutions  which  contain  copper  in  an 
abnormal  condition  is  that  in  which  copper  oxide  is  dissolved 
by  various  organic  acids  and  strongly  hydroxylated  com- 
pounds in  alkaline  solution,  as,  for  example,  in  Fehling's 
solution.  In  these  solutions  the  copper  may  not  be  complex 
in  the  sense  of  our  definition,  as  it  is  quite  probable  that 
only  the  usually-accepted  valencies  are  exercised,  but  it 
may  be  of  interest  to  add  some  account  of  such  solutions. 

Kahlenberg  (Zeit.  phys.  Chem.,  17,  586  (1895))  measured 
the  potential  of  the  cell 

Cu|CuS04  sol.|Fehling's  solution|Cu 

The  values  found  showed  that  only  minimal  amounts  of 
copper  ions  were  present  in  the  Fehling's  solution.  The 
depression  of  the  freezing  point  shown  by  Fehling's  solution 
was  also  smaller  than  that  calculated  from  the  separate 
ingredients. 

The  potentials  of  a  series  of  cells  of  the  type 


Cu|CuSO4,0'25    M. 


Alkaline   copper   solution 
containing  ' 
compounds 


containing  various  organic 


Cu 


were  also  measured,  the  organic  compounds  used  being  gly- 
collic  acid,  lactic  acid,  malic  acid,  citric  acid,  glycerol, 
erythrose,  mannose,  cane  sugar  and  biuret.  In  each  case  a 
large  potential  (0*2-0*5  volt)  was  produced,  showing  that  the 
copper  ion  concentration  in  the  alkaline  solution  was 
exceedingly  small. 

A  more  thorough  investigation  of  Fehling's  solution  was 
carried  out  by  Masson  and  Steele  (Trans.  Chem.  Soc,  1899, 
725).  Pure  cupric  tartrate  was  shaken  with  caustic  potash 
solution,  addition  of  potash  being  continued  until  the  pre- 
cipitate was  nearly  all  dissolved,  care  being  taken  that 
some  remained.  On  filtering  the  mixture,  a  clear  deep  blue 
solution  was  obtained  which  was  perfectly  neutral. 

Two  flasks  with  side  necks  were  connected  by  a  glass 


102  COMPLEX   IONS 

tube  of  narrow  bore  filled  with  a  solid  solution  which  was 
l'O  N.  with  respect  to  sodium  chloride  and  contained  12  per 
cent,  of  gelatine.  Platinum  electrodes  were  placed  in  the 
flasks,  both  of  which  were  filled  with  the  deep  blue  solution. 
The  apparatus  was  placed  in  cold  water  and  an  E.M.F. 
applied  to  the  electrodes.  Deep  blue  anions  moved  away 
from  the  kathode  through  the  tube,  while  the  kations  were 
evidently  colourless.  The  kathode  became  plated  with 
copper,  evidently  as  the  result  of  a  secondary  reaction  follow- 
ing upon  the  discharge  of  potassium  ions.  In  another 
experiment  the  anode  vessel  was  filled  with  copper  sulphate 
solution,  while  the  kathode  vessel  contained  the  deep  blue 
solution  as  before.  Two  blue  boundaries  now  appeared  on 
passing  the  current,  a  deep  blue  one  from  the  kathode  end 
and  a  pale  blue  one  from  the  anode  end. 

Similar  experiments  were  also  made  by  Kiister  (Zeit. 
Ehktrochemie,  4,  105). 

Masson  and  Steele  now  substituted  a  graduated  tube  for 
the  plain  one,  in  order  to  measure  the  velocities  of  the  two 
coloured  ions.  As  the  electrolysis  proceeded,  however,  it 
was  found  that  the  ratio  of  the  two  velocities  did  not  remain 
constant;  and  the  light  blue  boundary  suddenly  formed  a 
pale  blue  precipitate  at  a  certain  definite  point  in  the  tube 
where  it  had  been  expected  that  the  two  boundaries  would 
meet,  while  the  dark  blue  one  was  still  some  distance  away. 
The  dark  blue  solution  must  therefore  contain  a  faster 
colourless  ion  together  with  the  dark  blue  one,  which  is 
capable  of  giving  a  precipitate  with  cupric  ions.  This  is 
probably  the  tartrate  ion,  and  the  solution  must  contain 
some  potassium  tartrate. 

Next,  the  amount  of  alkali  required  for  production  of  the 
neutral  deep  blue  solution  was  determined  by  titrating  a 
weighed  quantity  of  cupric  tartrate,  the  alkali  being  added 
until  the  salt  just  dissolved  and  the  resulting  solution  being 
tested  with  litmus.  It  was  ascertained  in  this  way  that  the 
ratio  NaOH  :  CuC4H406  is  almost  exactly  1*25  :  1,  or,  in 
whole  numbers,  5  :  4. 


SOME   COBALT   AND   COPPER  SOLUTIONS     103 

Masson  and  Steele  considered  the  reaction  to  be  probably- 
represented  by  the  equation 

5KOH  +  4CuC4H406  =  K2C4H406  +  K3C12H7Cu4Ol8,5H20 

and  the  correctness  of  this  was  tested  as  follows.  On 
adding  alcohol  to  the  solution  a  crystalline  blue  precipitate 
is  thrown  down,  leaving  the  liquid  colourless.  The  liquid 
proved  to  contain  alkali  tartrate  in  about  the  quantity 
required  by  the  above  equation.  Analysis  of  the  precipitate 
showed  that  its  composition  agrees  with  the  formula 
K3Ci2Cu4H7Ol8,5H20.  Whether  all  the  water  is  present  as 
water  of  crystallisation  is  uncertain.  From  a  solution  of  this 
compound  the  silver  salt  was  precipitated,  amongst  others, 
and  analysis  of  it  gave  results  agreeing  with  the  formula 

Ag3C12Cu4H7O18,10H2O 

Little  is  known  of  the  stability  of  the  ion,  Ci2Cu4H70i8"', 
which  is  probably  produced,  save  that  it  does  not  yield 
cupric  hydroxide  with  caustic  alkali,  but  does  give  copper 
sulphide  on  treatment  with  hydrogen  sulphide. 


CHAPTER  X 

SOME   SPECIAL  CASES   OF   EQUILIBRIUM 

A.  Equilibrium  between  Metals  in  Different  Stages  of 
Oxidation. 

If  a  metal  forms  two  series  of  salts,  there  must  be  an 
equilibrium  in  the  system  containing  the  metal  and  its  two 
ions.  Thus,  if  we  place  a  solution  of  mercuric  nitrate  over 
mercury,  the  reaction 

Hg(N03)2  +  Hg  =  Hg2(N03)2 

occurs  to  a  considerable  extent.  The  presence  of  mercurous 
nitrate  in  the  liquid  can  be  readily  proved  by  adding  potas- 
sium chloride  when  calomel  is  precipitated. 

We  know  from  thermodynamic  considerations,  however, 
that  no  reaction  can  proceed  to  absolute  completion,  and 
accordingly  the  present  one  must  be  regarded  as  leading  to 
a  condition  of  equilibrium.  Assuming  that  both  salts  are 
equally  ionised,  which  is  sufficiently  near  the  truth,  the 
reaction  in  the  solution  may  be  represented  by  the  equation 

Hg"+Hg^Hg2" 

Since  liquid  mercury  is  present,  its  concentration  is  con- 
stant, and  the  condition  of  equilibrium  is  given  by  the 
equation 

[Hg-]  =  *[Hg2-] 

For  the  sake  of  clearness  in  the  example  we  have  antici- 
pated the  proof  of  the  constitution  of  the  mercurous  ion. 

From  the  above  equation  for  the  reversible  reaction  we 
may    draw   the   important   general  conclusion   that  a   salt 

104 


SOME  SPECIAL  CASES   OF  EQUILIBEIUM     105 

corresponding  to  the  highest  stage  of  oxidation  of  a  metal 
can  exist  in  the  pure  state — subject  to  its  dissociation  into 
metal  and  non-metal — in  absence  of  the  free  metal ;  while 
salts  corresponding  to  lower  stages  of  oxidation  cannot  exist 
at  all  in  the  pure  state  (saving  in  the  metastable  condition, 
such  as,  for  example,  the  state  of  solid  calomel)  since  they 
spontaneously  decompose  to  some  extent  into  the  metal  and 
a  salt  corresponding  to  a  higher  stage  of  oxidation.  Thus 
Behrend  (Zeit.  phys.  Chem.,  11,  474  (1893))  found  that 
mercurous  iodide  decomposed  on  solution  in  water  into 
mercury  and  mercuric  iodide.  This  decomposition  was 
further  studied  by  Ogg  (Zeit.  phys.  Chem.,  27,  285  (1898)). 
The  decomposition  of  calomel  into  mercury  and  mercuric 
chloride  was  referred  to  by  Kichards  (Zeit.  phys.  Chem., 
24,  39). 

A  very  thorough  study  of  the  equilibria 

Hg2"^Hg"  +  Hg 
and  Cu2"  ^  Cu"  4-  Cu 

was  made  by  Abel  (Zeit.  anorg.  Chem.,  26,  361  (1901)). 

Abel's  first  experiments  were  made  with  a  view  to 
ascertaining  the  value  of  the  equilibrium  constant  for  the 
reaction 

Hg2"^Hg"+Hg 

which  is  given  by  k  =  rjf.J 

A  solution  of  mercuric  nitrate  in  ca.  0*3  N.  nitric  acid 
was  shaken  with  mercury  in  a  thermostat  in  an  atmosphere 
of  carbon  dioxide.  A  portion  of  the  resulting  solution  was 
pipetted  out  and  the  mercurous  mercury  precipitated  with 
potassium  chloride  and  weighed.  The  filtrate  was  treated 
with  hypophosphorous  acid,  which  reduced  the  mercuric 
mercury  to  the  mercurous  condition,  so  that  a  further  quan- 
tity of  calomel  was  precipitated.  This  was  also  weighed. 
The  following  table  shows  the  results  obtained  at  25° : — 


106 


COMPLEX   IONS 


HgNOg 

cone. 

Hg(N03)2 
cone. 

.          [HgN03] 
k~  [Hg(N03)2] 

[HgN03]2 
*  -[Hg(N03)2] 

0-05163 
0-10042 
0-11059 

0000216 
0-000419 
0-000461 

239-03 

239-7 

239-9 

12-3 
24-2 
26-5 

The  concentrations  are  the  total  mercurous  and  mercuric 
contents  respectively,  calculated  in  terms  of  the  formulae 
HgN03  and  Hg(N03)2.     Thus  the  degrees  of  dissociation  are 


taken  as  equal.     The  fact  that  the  ratio 


is  con- 


[HgNOJ 
[Hg(N03)2] 

stant  shows  that  the  mercurous  ion  consists  of  two  mercury- 
atoms,     k'  corresponds  to  the  formula  Hg*  for  the  mercurous 
ion,  as  will  be  evident  from  the  scheme 
2Hg'^Hg"+Hg 
Thus  the  mercurous  ion    has    the   formula   Hg2**   and  the 
constant 

i  =  tH&L] 

has  the  value  120  very  nearly. 

Abegg  and  Shukoff  (Zeit.  fur  Elektrochemie,  12  (1906)) 
showed  that  a  mercury  anode  dissolves  in  these  proportions. 

We  are  now  in  a  position  to  explain  several  remarkable 
facts  relating  to  the  behaviour  of  mercury  salts.  Thus,  since 
Hg2-  ^Hg-  +  Hg 

it  follows  that  if  mercuric  ions  be  removed  from  a  solution 
containing  mercurous  and  mercuric  ions  in  equilibrium  with 
mercury,  more  mercurous  ions  will  dissociate,  producing  a 
further  supply  of  mercuric  ions  and  free  mercury.  Thus,  if 
we  add  potassium  cyanide  to  a  solution  of  mercurous  nitrate 
the  mercuric  ions  present  will  form  mercuric  cyanide  which 
is  practically  undissociated,  and  the  Hg"  concentration  will 
become  very  small.  This  will  cause  nearly  complete  dis- 
sociation of  the  mercurous  ions,  so  that  the  substances  react 
almost  completely  so  as  to  produce  mercuric  cyanide,  potas- 
sium nitrate,  and  mercury. 


SOME  SPECIAL  CASES   OF  EQUILIBRIUM     107 

Similarly  we  can  understand  how  addition  of  a  chloride 
to  calomel  causes  precipitation  of  mercury.  The  foreign 
chloride  ions  cause  a  large  depression  in  the  (already  very 
small)  concentration  of  mercuric  ions,  and  this  causes  the 
mercurous  ions  to  split  up.  A  similar  result  is  produced  by 
the  addition  of  sodium  nitrite  to  mercurous  nitrate,  the 
mercuric  ions  being  removed  in  this  case  to  form  the  com- 
plex ion  Hg(N02y  (Pick,  loc.  cit.).  In  general,  then,  the 
addition  to  a  mercurous  salt  in  solution  of  any  substance 
which  removes  mercuric  ions  promotes  its  decomposition. 

Again,  we  can  throw  a  general  light  upon  the  behaviour 
of  mercurous  salts  with  hydrogen  sulphide.  Since  addition 
of  sulphur  ions  to  a  mercurous  solution  causes  precipitation 
of  mercuric  sulphide  and  mercury,  we  have  in  the  solution 
mercuric  ions  in  equilibrium  with  mercury,  and  therefore 
also  with  mercurous  ions.  Hence,  if  the  two  substances 
were  precipitated  together,  we  should  have  the  relation 

[Hg2"]_[Hg2-][SH_LHg2s 
[Hg-]  ~  [Hg"][S"]-LHgs 

__  (solubility  of  mercurous  sulphide)2  _  .  „ 
(solubility  of  mercuric  sulphide)2 

Thus,  if  the  solubility  of  mercuric  sulphide  were  j^th  of 
that  of  mercurous  sulphide,  the  two  sulphides  would  be 
precipitated  together,  i.e.  25°  would  be  the  transition 
temperature  in  the  system 

Hg2S^HgS  +  Hg 

The  fact  that  only  mercuric  sulphide  and  mercury  are  pre- 
cipitated shows  that  the  solubility  of  mercuric  sulphide  is 
less  than  TTTth  of  that  of  mercurous  sulphide,  and  that 
mercurous  sulphide  is  therefore  unstable,  and  would 
spontaneously  decompose  into  mercuric  sulphide  and 
mercury. 

The   determination   of  the  constant  >J-U  is  also  im- 

LH§  J 
portant  in  relation  to  the  calomel  electrode.     A  calculation 
of  the  concentrations  of  mercurous  and  mercuric  ions  in  the 


108  COMPLEX   IONS 

normal  calomel  electrode,  based  upon  various  measurements 
by  other  observers,  was  given  by  Sherill  (Zeit.  phys.  Chem., 
43,  711  (1903)).  Later  the  subject  was  specially  studied  by 
Ley  and  Heimbucher  {Zeit.  fur  Elektrochemie,  10,  301  (1904)), 
who  measured  the  E.M.F.  of  the  cell 


Hg|Hg2Cl2,  0-1  N.KC1|0-1  N.  Hg^10*>* 


Hg 


In  order  to  ascertain  the  degree  of  dissociation  of  the 
mercurous  perchlorate,  a  series  of  measurements  of  its  con- 
ductivity was  made.  A  correction  was  applied  for  the 
hydrolysis  which  the  salt  undergoes  in  solution,  the  con- 
centration of  free  perchloric  acid  being  measured  by  deter- 
mining the  rate  of  hydrolysis  of  cane  sugar  in  a  solution  of 
the  salt.  (Unfortunately  the  calculation  as  printed  in  the 
original  paper  contains  a  misprint.) 

On  the  assumption  that  the  hydrolysis  is  represented  by 
the  scheme 

Hg2(C104)2  +  H20  =  Hg2(OH)C104  +  HCIO* 
Ley  and  Heimbucher  calculated  that  a  0*1  N.  solution  of 
mercurous  perchlorate  contains  0*047  gram  molecule  of 
unhydrolysed  salt,  and  is  0*035  M.  with  respect  to  mercurous 
ions.  The  correction  for  hydrolysis  is  small,  and  if  the 
scheme  shown  above  does  not  represent  the  reaction,  the  error 
cannot  be  great. 

The  two  electrode  vessels  were  connected  through  a 
solution  of  potassium  nitrate  with  a  view  to  minimising  the 
liquid  potential. 

Thus  it  was  found  that  the  concentrations  of  mercurous 
ions  in  the  decinormal  electrode  and  in  the  normal  one 
are  respectively  2*0  X  10"16  and  3*5  X  10"18.1     Hence  the 

1  From  these  figures  Ley  and  Heimbucher  calculated  the  solubility  of 
calomel.  Calling  the  solubility  product  L,  and  the  solubility  in  water  s, 
we  have 

4s3  =  L  =  [Hg2-][C1']2  =  2-0  x  10-1G(0-086)2 

for  the  decinormal  electrode,  and  similarly, 

4s3  =  3-5  x  10-"(0-75)2 
for  the  normal  electrode.     These    equations  give  s  =  0*72  x  10  ~6   and 
s  =  0*79  x  10  ~6  gram  molecules  per  litre  respectively. 


SOME   SPECIAL  CASES   OF   EQUILIBKIUM     109 

concentrations  of  the  mercuric  ions  are  1*7  X  10 ~18  and  3*1 
X  10"20. 

Abel  (loc.  cit.)  also  studied  the  equilibrium  existing 
between  cuprous  ions  on  the  one  hand  and  cupric  ions  and 
copper  on  the  other.  The  reaction  is  probably  represented 
by  one  of  the  two  following  schemes  : — 

(1)  Cu"  +  Cu^2Cir 

(2)  Cu"  +  Cu^Cu2" 

corresponding  to  which  we  obtain  the  constants 

*-ggl    (Dand*'=[gi     (2) 

The  equilibrium  is  thus  independent  of  the  anion,  and  in 
cases  where  this  does  not  appear  to  be  so,  we  have  reason  to 
believe  that  the  disturbance  is  caused  by  complex  formation. 
Thus,  cupric  chloride  in  acid  solution  in  contact  with  copper 
gives  a  colourless  solution  in  which  no  cupric  ions  can  be 
recognised,  while  copper  sulphate  under  the  same  conditions 
shows  little  change.  Hence  we  may  consider  it  probable 
that  in  the  chloride  solution  a  far-reaching  complex  forma- 
tion has  occurred  in  which  the  cuprous  ion  takes  part,  thus 
causing  practically  all  the  cupric  ions  to  become  reduced. 
This  complex-formation  was  subsequently  recognised  and 
investigated  by  Bodlander  and  Storbeck  (Zeit.  anorg.  Chem., 
31  (1902),  pp.  1,  458). 

Abel  found  that  complex-formation  also  occurs  in  the 
sulphate  solution,  and  the  investigation  of  the  cupro-cupric 
equilibrium  proved  to  be  a  matter  of  extreme  difficulty. 
The  constitution  of  the  cuprous  ion  is  still  uncertain. 
For  details  of  the  subject  the  reader  is  referred  to  the 
original  papers. 

One  other  point  of  interest  may  be  referred  to  in  connec- 
tion with  the  subject. 

In  contrast  with  the  behaviour  of  mercury,  a  solution 
containing  either  cuprous  or  cupric  ions  yields  when  treated 
with  hydrogen  sulphide  a  precipitate  consisting  of  cuprous 
and  cupric  sulphides  together.     Thus  the  transition  point  for 


110  COMPLEX   IONS 

the  system  cupric  sulphide,  cuprous  sulphide,  and  sulphur  lies 
at  about  the  ordinary  temperature.      We  may  represent  the 
reaction  provisionally  by  the  following  equation  : — 
2Cu"-f-S"^2Cu-  +  S 

which  gives  the  equilibrium  constant 

\  _  [Ou"]a [SI  _  [Cu"]*[S'T 
K  ~      [Cu-]2       "  [Cu-]2[S"] 

This  gives  the  special  relation 

7,  _  ^2cuS 

Lcu2s 

since  the  solution  is  saturated  with  respect  to  both  sulphides. 
The  last  equation  holds  good  whether  we  take  the  formula  of 
the  cuprous  ion  as  Cu*  or  Cu2",  providing  the  proper 
dimensions  are  given  to  L. 

A  further  interesting  case  of  equilibrium  between  salts 
corresponding  to  different  stages  of  oxydation  of  a  metal  is 
that  of  the  iodides  of  thallium.  This  was  exhaustively 
studied  by  Abegg  and  Maitland  (Zeit.  anorg.  Ohem.,  49,  341 
(1906)). 

When  shaken  with  solutions  of  iodine  in  carbon 
disulphide,  carbon  tetrachloride  or  aqueous  potassium  iodide, 
thallous  iodide  takes  up  iodine,  yielding  one  of  two  solid 
products  according  to  the  concentration  of  iodine.  These 
two  solid  products  are  (1)  T16I8  and  (2)  T1I3.  The  transition 
iodine  pressure  at  25°  was  determined  for  the  two  reactions 

(1)6T1I  +  I2   ^T16T8 
(2)Tl6I8  +  5I2^6Tir3 

In  the  case  of  the  non-aqueous  solvents,  the  corresponding 
concentration  of  aqueous  iodine  is  obtained  by  multiplying  the 
experimentally  found  value  by  the  distribution  coefficient. 

Thus  a  large  quantity  of  thallous  iodide  was  shaken  for 
seven  days  at  25°  with  a  solution  of  iodine  in  carbon 
disulphide  containing  initially  32*5  millimolecules  of  iodine 
per  litre.  After  shaking,  the  titre  was  found  to  have  fallen 
to  4*475  millimolecules  per  litre.     The   carbon  disulphide 


•    SOME   SPECIAL   CASES   OF  EQUILIBRIUM     111 

solution  was  now  diluted  slightly,  and  the  shaking  continued 
for  seven  days  more.  At  the  end  of  this  time  the  titre  was 
again  4*475  millimolecules  per  litre,  so  that  iodine  had 
separated  out  from  the  solid  phase  until  this  concentration 
was  reached  in  the  solution.  This  is  therefore  the  concen- 
tration corresponding  to  equilibrium  between  the  solids 
Til  and  T16I8.  Multiplying  the  iodine  concentration  by  the 
distribution  coefficient,  - J0,  we  obtain  for  aqueous  solution 
the  equilibrium  concentration 

4*475 

— — =  0*76  X  10     mols.  per  litre  of  water. 

590  X  1000 

In  accordance  with  this  result,  the  solid  T16I8  was 
obtained  by  treating  thallous  iodide  with  a  solution  of  iodine 
in  aqueous  potassium  iodide.  Starting  with  this  body  and 
carbon  disulphide,  the  same  iodine  titre  as  before  was 
obtained,  showing  that  the  solid  oxydation  product  in  the 
previous  experiment  was  really  T16I8.  In  a  similar  manner 
it  was  shown,  using  carbon  tetrachloride  solutions,  that  the 
equilibrium  concentration  in  water  for  the  reaction 

T16I8  +  5I2^6T1I3 

is  3*3  x  10"4  gram  molecules  per  litre. 

In  order  to  ascertain  whether  T1I3  was  the  highest 
oxydation  product,  solid  T1I3  was  shaken  with  a  saturated 
solution  of  iodine  in  carbon  tetrachloride.  The  concentration 
of  the  solution  remained  unaltered,  showing  that  the  system 
T1I3  +  I2  is  stable,  and  T1I3  is  the  highest  iodide  that  exists 
at  25°. 

The  latter  compound  may,  theoretically,  be  either  of  two 
possible  isomerides,  namely,  thallous  triiodide,  Til,  I2,  corre- 
sponding to  the  triiodides  of  the  alkali  metals,  and  yielding 
the  complex  ion  I3',  or  thallic  iodide,  yielding  the  ions  Tl— 
and  31'. 

A  series  of  experiments  showed  that  in  solution  this  sub- 
stance exists  simultaneously  in  both  forms,  so  that  it  is 
apparently  an  example  of  inorganic  tautomerism.  From  its 
small  solubility,  and  the  fact  that  it  is  isomorphous  with 


112  COMPLEX  IONS 

caesium  triiodide  (Wells  and  Penfield,  Zeit.  anorg.  Chem.,  6, 
312  (1894)),  it  appears  probable  that  the  solid  is  thallous 
triiodide. 

When  thallous  iodide  is  shaken  with  iodine  and  potassium 
iodide,  a  certain  amount  of  thallium  goes  into  solution.  Both 
alkali  iodide  and  iodine  play  an  essential  part  in  this  reaction, 
which  is  thus  to  be  regarded  as  caused  by  the  formation  of  a 
complex  thallic  ion.  In  the  following  calculations  the 
formula  T1I4'  is  assigned  to  this  ion,  and  the  results  show 
that  the  formula  is  the  correct  one. 

Solutions  of  potassium  iodide  of  various  concentrations 
(Column  II.)  were  shaken  with  thallous  iodide  and  iodine 
at  25°.  The  iodine  enters  into  three  reactions,  viz.  (1)  it 
combines  with  the  I'  ions  produced  by  the  potassium  iodide, 
forming  the  complex  ion  I3'  iu  the  manner  found  by  Jakowkin. 
We  may  call  this  portion,  for  convenience,  "Jakowkin 
iodine."  (2)  Another  portion  of  the  iodine  converts  the 
thallous  iodide  into  one  of  the  solids  T16I8  or  T1I3.  (3)  A 
further  portion  of  the  iodine  enters  into  combination  with 
thallium  in  solution  forming  the  complex  ion  T1I4'.  Finally 
the  remaining  iodine  exists  in  solution  in  the  free  state. 

The  concentration  of  this  free  iodine  (Column  V.)  was 
determined  by  shaking  the  liquid  with  carbon  tetrachloride 
or  carbon  disulphide.  This,  as  we  have  already  seen, 
determines  the  composition  of  the  solid  phase  (Column  III.). 

The  oxydation  potential  of  the  solution  was  measured 
against  the  1*0  N.  calomel  electrode.  This  gives  the  con- 
centration of  the  I'  ions,  since  the  oxydation  potential,  e0,  in 
the  equation 

e  =  e0  +  0-059  log10^^ 

had  been  previously  determined  by  Maitland  {Zeit.  fur 
Elektrochemie,  12, 263  (1906)).  Its  value,  putting  the  E.M.F. 
of  the  1-0  N.  calomel  electrode  equal  to  0,  is  +  0'341  volt, 
whence 

e  =  0-341  +  0-059  logw  ^] 


SOME   SPECIAL  CASES   OF  EQUILIBRIUM     113 

Thus  in  a  solution  in  which  the  free  iodine  concentration 
has  been  determined  by  distribution  we  can  calculate  [I']. 
The  values  thus  obtained  are  given  in  Column  VIII.  These 
values  must  be  equal  to  the  total  concentration  of  potassium 
iodide,  less  the  concentration  of  the  iodine  ions  that  have 
combined  with  iodine  to  form  the  ion  I3',  and  the  iodine  ions 
that  have  combined  with  T1I3  to  form  the  complex  ion 
T1I4'. 

The  iodine  (I2)  concentration  found  by  titration 
(Column  IV.)  consists  of  the  free  iodine,  the  "  Jakowkin  " 
iodine  and  the  iodine  which  separates  from  the  neutral  part 
(TII3)  of  the  complex  ion  T1I4'.  The  concentration  of  free 
iodine  may  be  neglected  compared  with  the  last  two  concen- 
trations, so  that  the  I2-titre  is  practically  equal  to  the 
concentration  [I3']  plus  the  concentration  [T1I4'].  Each  of 
these  last  two  terms  contains  one  iodine  ion  which  has  been 
taken  from  the  original  potassium  iodide,  and  hence  the 
difference  between  the  original  concentration  of  potassium 
iodide  (Column  II.)  and  the  I2-titre  gives  us  the  remaining 
free  potassium  iodide  concentration.  Multiplying  this  by 
the  degree  of  dissociation  taken  from  conductivity  data  for 
potassium  iodide  solutions,  we  obtain  the  concentration  of 
iodine  ions  (Column  IX.)  which  should  agree  with  the  value 
in  Column  VIII.  In  order  to  obtain  the  value  of  the  degree 
of  dissociation,  a,  the  concentration  was  taken  as  that  of  the 
total  potassium  in  the  solution  (KI  +  KI3  -f  KTII4),  the 
error  thus  introduced  being  quite  inconsiderable.  The  agree- 
ment between  the  values  in  Columns  VIII.  and  IX.  is  quite 
good,  and  thus  affords  evidence  for  the  correctness  of  the 
hypothetical  formula  Til/  for  the  complex  ion. 

Further,  the  value  of  the  constant 

1  ~   M 

was  calculated  as  follows.  The  concentration  [I2]  is  known 
from  the  distribution  experiments  (Column  V.).  [I']  is 
obtained  by  subtracting  the  I2-titre  (Column  IV.)  from  the 


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SOME  SPECIAL  CASES   OF  EQUILIBRIUM     115 

original  concentration  of  potassium  iodide,  and  (for  greater 
accuracy)  adding  the  concentration  of  free  iodine,  since  the 
I2-titre  includes  this.  [I3']  was  found  by  subtracting  [I2] 
(Column  V.)  together  with  the  total  concentration  of  thallium 
in  the  solution  (=  [T1I4'] :  Column  VI.)  from  the  I2-titre. 
The  values  of  [I']  and  [la']  thus  found  are  really  those  of  the 
total  concentrations  of  the  corresponding  potassium  salts, 
and  should  therefore  be  multiplied  by  the  respective  degrees 
of  dissociation  in  order  to  yield  the  true  concentrations  of 
the  ions ;  but  since  only  the  ratio  enters  into  the  formula, 
and  the  two  salts  are  practically  equally  dissociated,  no 
correction  is  necessary.  Thus  in  terms  of  the  values  in  the 
various  columns,  we  have 

_V(H-IV  +  V) 
"*  -   IV  -  V  -  VI 

The  values  of  kj  found  in  this  way  are  given  in  Column  X., 
and  show  excellent  agreement  with  one  another,  being 
more  concordant  than  the  values  found  by  Jakowkin 
(0*77  —  1*44  X  10 ~3),  but  of  about  the  same  mean  value. 
Since  this  result  depends  upon  the  twofold  application  of 
the  hypothesis  that  the  ion  T1I4'  is  present,  it  constitutes  a 
further  confirmation  of  the  correctness  of  this  assumption. 

Besides  being  a  measure  of  the  ratio  VM/P'],  the 
oxydation  potential  simultaneously  shows  the  ratio 
[T1"']/[T1*],  according  to  the  relation 

[T1-] 

Spencer  and  Abegg  (Zeit.  anorg.  Chem.,  44,  379  (1905)) 
showed  that  e0  in  this  formula  has  the  value  +  0*916  volt. 

The  values  of  logi0  rL.ji  calculated  from  this  expression  are 

given  in  Column  XL 

In  all  the  solutions  the  Tl-  concentration  is  exceedingly 
small  compared  with  the  Tl*  concentration.  Since  no  thallous 
thallium  is  analytically  recognisable  in  the  solution,  while 
considerable  quantities  of  thallic  thallium  are  known  to  be 


e  =  e0  4-  0-0295  log 


116 


COMPLEX   IONS 


present,  this   gives  us  an  insight   into  the  stability  of  the 
thallic  complex  ion,  which  is,  in  fact,  very  great. 

So  far  we  have  obtained  only  the  ratio  of  the  concentra- 
tions of  the  two  thallium  ions.  The  absolute  concentrations 
can  be  readily  calculated,  however,  for  those  solutions  which 
are  in  equilibrium  with  solid  thallous  iodide  (Nos.  1,  2  and  3). 
The  solubility  of  thallous  iodide  was  determined  at  18°  and 
2015°  by  Kohlrausch  and  Bottger  respectively  (Landolt  and 
Bornstein,  3te  Auf.).  By  extrapolation  from  their  results 
Abegg  and  Maitland  obtained  the  value  2*4  x  10~4  gram 
mols.  per  litre  at  25°,  from  which  we  have 


whence 


L=[Ti-][I']=5-8  x  10 

pti.-i-S-sxio-8 


Thus,  using  the  values  of  [I']  in  Column  VIII.,  we  can 
calculate  [T1-]  and  [Ti~]  for  Nos.  1,  2  and  3.  The  values 
of  log10  [T1-]  and  logi0[Tl*-]  are  shown  in  Columns  XII.  and 
XIII.  respectively. 

We  can  now  calculate  the  stability  constant  of  the  ion 
TII4',  and  in  so  doing  we  apply  a  rigorous  test  to  the  correct- 
ness of  the  formula.      From  the  law  of  mass-action  we  have 


h  = 


[Tll4r] 
[Tl-][r 


The  concentration  of  the  ion  T1I4'  is  given  by  the  total 
thallium  content  of  the  solution  (Column  VI.),  since  no  other 
compound  of  thallium  and  iodine  possesses  an  analytically 
measurable  solubility  in  water.  Thus,  using  the  values 
already  found  for  [T1-]  (Column  XIII.)  and  [I']  (Column 
VIII.),  the  values  of  h  are  obtained  for  Nos.  1,  2,  and  3. 
These  are  given  in  Column  XIV. 

ht  must  be  constant  also  in  those  solutions  which  are  not 
in  equilibrium  with  solid  thallous  iodide,  so  that  we  can  now 
calculate  the  Tl,,#  concentration  in  these  solutions,  since 
[Til/]  and  [I']  are  known:  and  we  thus  also  obtain  the 
values  of  [Tl*]  for  these  solutions,  using  the  ratio  in  Column 


SOME   SPECIAL  CASES   OF  EQUILIBBIUM     117 

XI.  The  Tl*"-  and  Tl*- concentrations  thus  found  are  given 
in  Columns  XII.  and  XIII. 

Another  relationship  can  be  traced  in  the  solutions 
which  are  not  in  equilibrium  with  TIL  The  complex  ion 
T1I4'  is  in  equilibrium  with  undissociated  T1I3  and  V  accord- 
ing to  the  scheme 

TlI4'^TlI3  +  r 

whence  E™p  =  &n[TlI3] 

The  ratio  [T1I4']/[I']  is  thus  proportional  to  the  concentration 
of  undissociated  T1I3.  The  values  of  Jcn  x  [T1I3],  obtained 
by  dividing  the  total  thallium  concentration  (Column  VI.)  by 
the  I'-concentration  (Column  VIII.)  are  shown  in  Column 
XV.  In  accordance  with  the  law  of  mass  action,  these 
values  are  constant  for  solutions  in  equilibrium  with  solid 
T1I3.     Further,  since 

T1I3  +  5T1I^T16T8, 

we  obtain  [TH3]  =  T^ffis 

and  the  concentrations  on  the  right-hand  side  of  this 
equation  become  constant  when  the  solution  is  in  equilibrium 
with  Til  and  Tl6l8  simultaneously.  Hence  kn  X  [T1I3]  should 
also  be  constant  in  these  solutions,  and  experiment  shows 
that  this  is  the  case  (Nos.  1,  2  and  3).  A  comparison  of  the 
values  of  kn  X  [T1I3J  shows  that  in  solutions  in  equilibrium 
with  Til  and  Tl6l8  the  concentration  of  T1I3  is  about 

nnQ      2-9  xlO"2,. 
0*03  =  — zr-zr. —  times 
114 

that  in  solutions  saturated  with  respect  to  T1I3. 

Having  thus  obtained  a  measure  of  the  concentration  of 
undissociated  T1I3,  we  may  now  attain  a  similar  result  for 
Til.     Since 

T1I3^T1I  +  I2 
it  follows  that 

[Til]  =  const.  X  K^ 


118 


COMPLEX   IONS 


so  that  by  dividing  the  values  in  Column  XV.  by  the  corre- 
sponding concentrations  of  free  iodine  (Column  V.)  we  obtain 
a  series  of  values  which  are  proportional  to  [Til],  (Column 
XVI.).  These  should  be  constant  and  maximal  in  solutions 
in  equilibrium  with  solid  Til.  This  is  also  actually  the  case 
(Nos.  1,  2  and  3).  Numbers  4,  7  and  8  show  values  which 
are  as  high  or  a  little  higher,  but  the  error  is  not  large. 
Also  these  abnormal  values  occur  in  solutions  which  are 
rather  concentrated  with  respect  to  potassium  iodide. 

Comparing  these  values,  we  find  that  the  value  of  the 
Til-concentrations  is  always  a  very  appreciable  fraction  of 
its  saturation  concentration.  The  lowest  concentration, 
namely,  that   in   saturated  iodine   solution,   is   about   0*22 

(  =  — -  )  of  the  saturation  value.  Thus  T1I3,  even  in  equi- 
librium with  solid  iodine,  acts  as  Jth  saturated  Til,  which 
agrees  with  the  view  of  Wells  and  Penfield  (loc.  cit.)  as  to  its 
constitution.  This  may  be  further  tested  by  calculating  the 
solubility  product  [Tr][I3'],     By  means  of  the  equation 

MP'] 

[h'l 

we  can  calculate  the  value  of  [I3']  from  the  data  in  Columns 
V.,  VIII.  and  X.  The  values  of  the  solubility  product  in  the 
solutions  saturated  with  T1I3  are  given  in  Column  XVII.,  and 
show  very  satisfactory  concordance,  thus  forming  additional 
evidence  for  the  view  that  T1I3  exists  for  the  most  part  in 
the  form  of  thallous  triiodide.  The  tautomeric  character  of 
the  substance  is  clearly  shown,  however,  by  the  fact  that  it 
readily  yields  the  complex  thallic  ion  T1I4\ 


kj  = 


B.  The  precipitation  of  sulphides. 

The  precipitation  of  metallic  sulphides  by  hydrogen  sul- 
phide has  a  special  interest  on  account  of  the  great  importance 
of  the  subject  in  analysis.  While  the  analytical  procedure 
has  been  built  up  empirically  upon  experience  of  its  results, 
it  is  highly  desirable  to  give  the  processes  a  theoretical 
groundwork. 


SOME   SPECIAL   CASES   OF  EQUILIBRIUM     119 

In  precipitating  the  sulphide  of  a  mono-,  di-  or  tri-valent 
metal  respectively,  the  reactions  are  represented  by  the 
following  equations : — 

(1)  2Me-  +  S"^Me2S 

whence  rii/  01  ■  =  h 

[Me2S] 

(2)  Me-  +  S"^MeS 

whence  lMei[S"]  =  ,a 

[MeS] 

(3)  2Me-  +3S"^Me2S3 

whence  PgflgT  -I, 

[Me2S3] 

The  concentration  of  the  sulphur  ions  is  connected  with 
the  concentration  of  hydrogen  sulphide  as  follows.  Hydrogen 
sulphide  dissociates  in  two  stages  according  to  the  equations 

H2S^HS'  +  H- 
HS'  ^S"  +  H- 

whence  L_JL_J  =  h 

[HJ[S"]      ,  , 
and  LgLJ  =  h 


or 


[H2S]     -*1*4 


Thus  [8"]=*iTV.^  =  A'^ 


Substituting,  we  obtain 


[Mef  [H^S]  _ 
[H]2        ~     ' 

[Me-1[H2S]  _ 
[Of  a 

[Me-]2[H2SP_ 


120 


COMPLEX   IONS 


and  the  corresponding  solubility  products  are 

U  =  [Me-]2[S"]  =  ffK, 
L2  =  [Me-][S"]  =  k'K2 
L3  =  [Me-]2[S"]3  =  ^3K3 

ku  the  first  dissociation  constant  of  hydrogen  sulphide, 
was  determined  by  Auerbach  (Zeit.  phys.  Chem.,  49,  217 
(1904))  from  measurements  of  the  conductivity  of  its  aqueous 
solution.  The  first  dissociation  only  was  taken  into  account, 
since  the  second  dissociation  constant  of  a  weak  dibasic  acid 
is  always  minute  compared  with  the  first  one.  In  this  way 
Auerbach  found  a  series  of  values  of  &/  for  solutions  of 
various  concentrations  of  hydrogen  sulphide  which  showed 
excellent  agreement  amongst  themselves,  and  gave  the  mean 
value  0'91  x  10-*  at  18°. 

fe',  the  second  dissociation  constant,  has  also  been 
measured  (Knox,  Trans.  Farad.  Soc,  Vol.  IV.  Part  I.  (1908)) 
by  a  method  which  will  be  discussed  later.  Its  value 
is  1-2  X  10~15  at  25°.  Hence  h^  .hi  =  U  =  0*91  x  10~7 
X  1*2  X  10-15  =  1-09  x  10-22  at  25°  very  nearly,  and 

L,  =  1*09  X  10-22 .  Ki 
L2  =  1-09  x  10~22.K2 
L3  =  1*30  x  10-66.K3 

Thus,  if  we  know  L  we  can  calculate  K,  and  vice  versa. 
These  constants  have  been  measured  for  nearly  all  the  heavy 
metals. 

Bernfeld  (Zeit.  phys.  Chem.,  25,  46  (1898))  measured  the 
potentials  of  cells  of  the  type 

M|M*S„  +  l'O  N.  NaHS  +  H2S  (1  atmos.)|l'0  N.  E 

using  the  metals  silver,  lead  and  bismuth.  From  the  experi- 
mentally determined  E.M.F/s  the  concentrations  of  the  metal 
ions  were  calculated,  using  the  known  values  of  their 
respective  electrolytic  potentials.  Bernfeld  found  the  con- 
centrations of  the  metal  ions  in  a  1*0  N.  sodium  hydro- 


SOME  SPECIAL   CASES   OF  EQUILIBEIUM     121 

sulphide  saturated  with  hydrogen  sulphide  at  a  pressure  of 
one  atmosphere  and  with  the  metallic  sulphide  to  be 

[Ag-]  =  3-4  X  10-22 
[Pb-]  =  1-45  x  10-5 
[Bi-]  =  0-7  X  10-26 

It  has  since  been  shown,  however,  that  the  value  for  lead  is 
incorrect.     This  will  be  discussed  later. 

Lucas  (Zeit.  anorg.  Ghem.,  41,  193  (1904))  measured  the 
solubility  of  silver  sulphide  in  potassium  cyanide,  and  using 
the  known  value  of  the  constant 

_  [Ag-][CNT 
*  -  [Ag(CN)3"] 

(Bodlander  and  Eberlein,  loc.  cit),  was  able  to  calculate  the 
concentration  of  the  silver  ions.  His  calculation  of  the 
concentration  of  the  sulphur  ions  is,  however,  incorrect.1 

Glixelli  (Zeit  anorg.  Chem.,  55,  297  (1907))  studied 
analytically  the  precipitation  of  zinc  sulphide  in  acid  and  in 
alkaline  solutions,  and  showed  that  in  acid  solution  the 
precipitation  leads  to  a  false  equilibrium,  the  reaction  coming 
to  a  stop  at  a  point  which  cannot  be  approached  from  both 
sides.     In  alkaline  solution  K2  =  5  X  10~5. 

A  very  thorough  study  of  the  behaviour  of  the  sulphur 
anion  was  made  by  Knox  (Trans.  Farad.  Soc,  Vol.  IV. 
Part  I.  (1908)),  who  determined,  amongst  other  things,  the 

1  Lucas  points  out  that  in  calculating  the  concentration  [S"]  we  must 
allow  for  the  hydrolysis  of  both  the  potassium  sulphide  and  the  potassium 
cyanide.    He  gives  the  equation 

[irnoHg 

[ON']  L  *  X  1U 

which  is  obviously  incorrect.  For  [E>]  we  should  read  [HON],  In  this 
case,  however,  we  could  only  solve  for  [OH']  by  putting  [OH']  =  [HON]. 
This  would  be  allowable  in  a  solution  containing  potassium  cyanide  alone, 
and  might  be  so  in  the  mixed  solution,  seeing  that  the  solubility  of  silver 
sulphide  in  potassium  cyanide  solutions  is  small.  Kecalculation  from 
Lucas's  experimental  results,  however,  showed  that  this  had  not  been 
done.  Lucas  does  not  give  the  method  by  which  his  calculations  were 
made. 


122 


COMPLEX   IONS 


value  of  the  second  dissociation  constant  of  hydrogen  sul- 
phide. This,  in  conjunction  with  the  value  of  the  first 
constant  found  by  Auerbach  (loc.  cit.)  enables  us  to  calculate 
K  and  L  for  the  various  sulphides,  the  concentrations  of 
whose  metal  ions  in  solutions  of  sodium  hydrosulphide  have 
been  determined  by  other  observers. 

Knox  began  by  studying  the  reaction  in  virtue  of  which 
mercuric  sulphide  is  dissolved  to  a  considerable  extent  by 
solutions  of  sodium  sulphide.  In  the  light  of  the  formula 
established  by  Knox,  this  reaction  may  be  regarded  as 
leading  to  the  formation  either  of  the  complex  salt  HgSSNa^, 
yielding  the  complex  anion  HgSS",  or  of  the  salt 
Na — S — Hg — S — Na,  in  which  only  the  usually-accepted 
valencies  are  exercised. 

The  following  table  shows  the  values  of  the  solubility  of 
red  and  black  mercuric  sulphide  in  sodium  sulphide  solutions 
at  25°:— 


Cone. 

Na2S 

Mol. /litre. 

HgS  (red) 
dissolved 
Mol. /litre. 

Ratio  HgS 
(red) :  Na2S. 

HgS(black) 
dissolved 
Mol. /litre. 

Ratio 
HgS  (black) 
HgS  (red) 

2030 

1-52 

1-015 

0-755 

0-50 

0-25 

0-10 

1-144 

0-7832 

0-4423 

0-2878 

0-1500 

0-04544 

0-008241 

0-5635 
0-5153 
0-4328 
0-3812 
0-3006 
0-1818 
0-0824 

0-8561 

0-5002 

0-3336 

0-1805 

0-05622 

0-01085 

1-09 
1-13 
1-16 
1-20 
1-24 
1-32 

The  fact  that  black  mercuric  sulphide  is  more  soluble  than 
the  red  variety  (the  solution  in  each  case  having  the  same 
constitution)  proves  that  the  black  form  is  the  unstable 
one.  This  is  supported  by  the  following  circumstances : 
(1)  when  hydrogen  sulphide  is  passed  into  the  above  solu- 
tions, black  mercuric  sulphide  is  precipitated.  (2)  The 
black  sulphide  is  slowly  converted  into  the  red  form  on 
standing  in  contact  with  the  solution. 

The  complex  formation  may,  as  usual,  be  represented  by 
the  scheme 

mHgS+?iS"^(HgSWS")n 


SOME   SPECIAL   CASES   OF   EQUltlBKIUM     123 
Applying  the  law  of  mass-action,  we  obtain 

[(HgS)m(S")»]  ~  * 
or  [(HgS)m(S")n]  =  K[HgS]-[S"J" 

In  saturated  solution  [HgS]m  is  constant,  so  that  the  solu- 
bility (which  is  practically  the  concentration  of  the  complex 
ion)  is  proportional  to  [S"]\ 

Now,   sodium    sulphide    hydrolyses    according    to    the 
equation 

Na2S  +  H20  ^  NaHS  +  NaOH 

or,  leaving  out  the  sodium  ions,  whose  concentration  remains 
practically  unchanged, 

S"  +  H20  ^  HS'  +  OH' 


Hence 


[HS'][OH']  _ 

[S"i      -kh 


kh  being  the  hydrolysis  constant  of  sodium  sulphide.  From 
this  equation  we  can  see  that  by  increasing  the  concentration 
of  hydroxyl  ions  we  shall  diminish  the  degree  of  hydrolysis 
of  the  sodium  sulphide,  thus  causing  [HS']  to  grow  smaller 
and  [S"J  to  increase  by  the  same  amount ;  and  since  the 
solubility  of  mercuric  sulphide  in  the  solution  is  pro- 
portional to  [S"]n,  addition  of  caustic  soda  should  increase 
this.  The  following  table  shows  the  solubility  of  red 
mercuric  sulphide  in  various  solutions  of  sodium  sulphide 
and  caustic  soda : — 


Cone. 

Na.S 

HgS  (red)  dissolved  in  Mols. /litre 

Ratio  HgS : 
Na2S  in 

Mol./litre 

In  pure 

N^S. 

With  0  5 

N.  NaOH. 

With  1 -ON. 
NaOH. 

With  4-48 
N.  NaOH. 

With  4-67 
N.  NaOH. 

With?-7N. 
NaOH. 

solutions  with 
1-1  N.  NaOH. 

1-015 

0-755 

0-50 

0-25 

0-10 

0-4423 

02878 

0-1500 

0-04544 

0-008241 

0-2483 
0-1106 
0-03962 

CO 
CO  O  CM  00  CO 

CO  -tf  CO  tH  O 

6  6  6  66 

0-435 

0-225 
0-0903 

09167 

0-4637 
0-2369 
0-09634 

0-903 

0-927 
0-948 
0-963 

124 


COMPLEX   IONS 


In  the  strongly  alkaline  solutions  the  concentration  of  HgS 
becomes  nearly  equal  to  that  of  Na2S,  so  that  if  each  HgS 
molecule  takes  up  one  sulphur  ion,  only  a  small  quantity  of 
sulphur  ions  can  remain  and  the  degree  of  hydrolysis  must 
be  small.  Thus,  unless  m  is  greater  than  one,  the  formula  of 
the  complex  salt  must  be  Na2HgS2  and  that  of  the  complex 
anion  HgS2". 

This  conclusion  was  supported  by  the  results  of  potential 
measurements.  Owing  to  the  difficulty  of  determining 
exactly  the  concentration  of  S"  ions,  the  application  of  this 
method  was  at  first  limited  to  the  measurement  of  the 
E.M.F.'s  of  cells  containing  equal  quantities  of  sodium 
sulphide  and  small  but  different  amounts  of  HgS,  thus 
allowing  only  of  the  calculation  of  m.  In  this  way  it  was 
found  that  m  =  1,  so  that  the  formula  for  the  complex  ion 
must  be  HgS2",  and  n  =  1  also.  Assuming  this  formula, 
the  potential  method  was  now  applied  as  follows : — 

The  complex  ion  must  dissociate  into  its  single  ion  and 
neutral  part  according  to  the  equation 

HgS2"^HgS  +  S" 

so  that  in  solutions  saturated  with  respect  to  HgS, 

[HgS2"]  =  K[HgS][S"]  =  ys"] 

since  the  concentration  of  HgS  is  constant. 

For  the  dissociation  of  HgS  the  mass-action  equation  is 

[HgS]  =  ^[Hg-HS"] 

and  since  HgS  is  constant,  this  gives 


[S"] 


[Hg"] 
Substituting  in  the  first  equation,  we  get 


[HgS2"]  = 


[Hg-]      [Hg-] 

Hence,  if  m  =  n  =  1,  the  product  [HgS2"][Hg"]  is  constant 
in  all  saturated  solutions.    [HgS2"]  is  practically  equal  to  the 


SOME   SPECIAL   CASES   OF   EQUILIBEIUM     125 

concentration  of  dissolved  HgS,  and  [Hg"]  can  be  found  by- 
measuring  the  potential  of  the  cell 

Hg|complex  solution|l'0  N.  E 

The  concentration  of  mercuric  ions  in  the  normal  electrode 
was  found  by  Ley  and  Heimbucher  (loc.  cit.)  to  be  3  x  10  ~20 
gram  ions  per  litre. 

Hence,  if  e  be  the  E.M.F.  of  the  cell  (the  normal  electrode 
being  positive) 

3  x  1(T20 


e  =  0-0295  log 


[Hg* 


The  following  table  shows  the  results  obtained  in  this 
way:— 


Cone.  Na2S 
Mol. /litre. 

Cone.  HgS2" 
=3  dissolved 
HgS  Mol./l. 

E.M.F. 
against 
1-0  N.  E. 

[Hg"]. 

Hg"J[HgS2"]=fc6 

2-030 

1-144 

-  0-9715 

3-53  x  10-53 

4-0  x  10-53 

1-52 

0-7832 

-  09650 

5-21  x  10-53 

4-1  x  10 -53 

1-015 

0-4423 

-  0-9570 

10-9  x  10- 53 

4-8  x  10  ~53 

0-755 

0-2878 

-  0-9515 

16-5  x  10- 53 

4-7  x  10-53 

0-50 

0-1500 

-  0-9455 

26-7  X  10-53 

4-0  x  10" 5J 

0-25 

0-04544 

-  0-9335 

58-5  x  10- 53 

2-7  X  10-53 

0-10 

0-008241 

-  0-9145 

300  X  10-53 

2-5  x  10-53 

No  attempt  was  made  to  allow  for  diffusion  potentials. 
Knox  states  that  the  E.M.F.'s  were  reproducible  to  within  a 
millivolt. 

The  concentrations  of  mercury  ions  in  these  solutions  are 
so*  small  that  the  ordinary  conception  of  a  potential  between 
a  solution  and  an  electrode  in  terms  of  the  kinetic  theory  of 
gases  and  solutions  breaks  down  entirely.  If  we  take  the 
number  of  molecules  in  a  gram  molecule  as  being,  in  round 
numbers,  1024,  we  see  that  a  solution  containing  10  ~53  gram 
ions  of  mercury  per  litre  is  equivalent  to  1029  litres  of  water 
containing  one  single  mercury  ion !  The  electrochemical 
reaction  must  therefore  be  looked  upon  as  produced  by  the 
other  ions  present  which  are  potentially  in  equilibrium  with 


126 


COMPLEX   IONS 


mercury  ions  at  this  concentration.  The  point  had  already 
been  discussed  by  Haber,  Bodlander,  Abegg  and  Daneel 
(Zeit.  fur  EleMrochemie,  10,  403,  604,  607,  609,  and  773 
(1904)).  (See  Le  Blanc,  Lehrbuch  der  Mehtrochemie,  4te 
Auf.,  p.  189.) 

From  the  equation 

[OH'][HS']=yS"] 
we  obtain  for  solutions  containing  no  added  H2S  or  NaOH 

[hst  =  hvn 

since  [OH']  =  [SH'] 

Further,  assuming  complete  electrolytic  dissociation  of  NaHS 
and  Na2S,  we  have 

[HS']  +  [S"]  =  a  -  b 

where  a  is  the  total  initial  concentration  of  Na2S  and  b  that  of 
the  dissolved  HgS,  i.e.  that  of  the  complex  salt.  From  these 
two  equations  we  get 

[HS']=-|  +  \/|2  +  ^>-&) 

and  [S"]  =a-&-[HS'] 

Thus  if  we  assume  a  value  for  hh}  we  can  find  [S"]  in  the 
solutions  used  in  the  above  measurements,  and  thus  also  L, 
the  solubility  product  of  mercuric  sulphide,  and  ks,  the 
stability  constant  of  the  complex  ion,  which  is  given  by  the 
equation 

ft  -   [HgS2"]  , 

•      [Hg][S'T 

From  Kiister's  measurements   (Zeit. 

(1900))  Knox  calculated  kh  =  0*274. 

unsatisfactory  results,  however,  when  inserted  in  the  above 

expressions,  and  as  the  solubility  and  potential  measurements 

show   that  a   definite   complex   ion,    HgS2",   predominates 

strongly  in  these  solutions  and  dissociates  according  to  the 

law  of  mass-action,  a  value  of  hh  was  found  by  trial  which 


phys.    Chem.}   30,   128 
This  value  gave  very 


SOME   SPECIAL   CASES   OF   EQUILIBRIUM     127 

gave   satisfactory   results.     The   following  table  shows  the 
results  of  Knox's  calculations : — 


Cone.  Na2S 
Mol. /litre. 


Cone.  S" 
grm.  ion/1. 


[Hg-][S"] 
—  L. 


[HgSa"] 
[Hg';][S"p 


fy  =  0  405.    This  gives  hydrolysis  in  0-05  M.  solution  =  90  per  cent. 


2-03 

0-456 

1-6  X  10  -53 

1-6    X  1053 

1-52 

0-356 

1-8  X  10  ~53 

1-2    x  1053 

1015 

0-252 

2-7  X  10  ~53 

0-64  x  10" 

0*755 

0-189 

3*1  X  10  ~« 

0-49  x  1053 

0-50 

0-125 

3-3  x  10  ~"53 

0-36  x  1053 

0-25 

0-0549 

3-2  x  10  ~53 

0-25  x  1053 

0-10 

0-0145 

4-4  x  10-« 

0-13  x  1053 

fc/t=l'0.,  This  gives  hydrolysis  in  0-05  M.  solution  =  95  per  cent. 


2-03 

0-320 

1-1  x  10  ~53 

3-2    x  10'3 

1-52 

0-243 

1-3  x  10  -53 

2-4    x  1053 

1-015 

0166 

1-8  x  10  ~53 

1-5    x  1053 

0755 

0-120 

2-0  x  10" 53 

1-2    x  1033 

050 

0-075 

2-0  x  10"53 

0-99  x  'W* 

0-25 

0-0402 

2-4  x  10  ~53 

0-48  x  1053 

0-10 

0*0072 

2-2  x  10  ~53 

0-53  X  1053 

kh  =  5.    This  gives  hydrolysis  in  0-05  M.  solution  =  99  per  cent. 


2-03 

0-118 

0-42  x  10  ~53 

23  X  1053 

1-52 

0-0848 

0-44  x  10  ~53 

21  x  1053 

1-015 

0-0537 

058  X  10 ~53 

14  X  1053 

0-755 

0-0372 

0-61  x  lO"53 

13  X  1053 

0-50 

0-0217 

0-58  X  lO"53 

12  X  1053 

025 

0-0076 

0-44  x  10  ~53 

13  X  1053 

0-10 

0-00176 

0-53  X  10  ~53 

9  X  1053 

k]t  =  10.    This  gives  hydrolysis  in  0-05  M.  solution  =  99*5  per  cent. 


2-03 

0-067 

0-24  X  10"53 

7-2  X  1054 

1-52 

0-048 

0-25  x  10"53 

6-5  x  1054 

1-105 

0-030 

0-33  x  10  ~53 

4-5  X  1054 

0-755 

0-022 

0-36  x  10  ~53 

3-6  x  1054 

0-50 

0-011 

0-29  X  10  ~53 

4-6  X  1054 

0-25 

0-0041 

024  x  10-53 

4-6  x  1054 

0-10 

0-00076 

0-23  X  10"53 

4-8  X  1054 

128 


COMPLEX   IONS 


We  may  therefore  take  as  a  probable  value 
^=10 

In  order  to  throw  further  light  upon  this  result  measure- 
ments were  made  of  the  speed  of  decomposition  of  diacetone 
alcohol  in  presence  of  caustic  soda  and  sodium  sulphide 
respectively.  The  reaction  mixture  was  placed  in  a  dilato- 
meter,  and  the  change  in  volume  noted  as  the  reaction 
proceeded.  In  this  way  it  was  shown  that  0*1  M.  and 
0'05  M.  solutions  of  sodium  sulphide  are  nearly  completely 
hydrolysed.  The  method  is  insufficiently  accurate  to  give 
the  degree  of  hydrolysis  to  within  one  or  two  per  cent.,  but 
it  is  certainly  greater  than  95  per  cent.,  and  thus  much 
higher  than  the  value  given  by  Kiister. 

It  is  interesting  to  notice  that  Knox  prepared  a  solid 
double  sulphide  of  sodium  and  mercury  which  has  the  com- 
position represented  by  the  formula  2Na2S,  5HgS,  3H20. 
This  is  a  further  case  where  the  solid  which  separates  from 
a  solution  has  a  different  composition  from  the  predominating 
component  in  the  liquid  (Chapter  VIII),  and  indicates  that 
probably  other  less  stable  complex  ions  are  present  to  some 
extent  in  the  solution. 

Having  found  the  value  of  7eh  we  can  now  calculate  the 
second  dissociation  constant  of  hydrogen  sulphide,  namely 

,     [H'3[S»] 

*  ~    [HS'J 
From  the  equations 

[H-][OH']  =^  =  l-2x  10"" 
and  [HS'][OH']  =  kh[S"] 


.  .  .  [H-][S"]      ,, 

we  obtain  rtran    =  #2  = 


[HS'j 


Since 


we  have 


*-  =  1-2 


ko      == 


h 
x 

1-2  x  10 


h 
10* 


and  kh  =10 


10 


=  1-2  x  10 


-15 


This  result  is  of  the  utmost  importance,  as  it  enables  us  to 


SOME  SPECIAL  CASES  OF  EQUILIBRIUM    129 

rs'i 

calculate  the  ratio  p-W^i  in  any  solution  in  which  we  know 
|±lbj 

the  value  of  [H*]  or  [OH'].     A  few  examples,  taken  from 

Knox's  paper,  will  make  this  clear. 

We  have  the  relationship 

[S»]   _  k2'  _  1-2x10-" 
[HS']      [H-]  [H-]        "Uilunj 

In  neutral  solution  ([OH']  =  1*1  x  10"7) 

[S"]  =  1-1  x  10"8[HS'] 
In  1-0  N.  acid  solution  ([OH']  =  1*2  x  11T14) 

[S"]  =  1-2  x  1(T15[HS'] 
In  1-0  N.  basic  solution  ([OH']  =  1*0) 

[S"]  =  0-1  [HS'] 
and  in  10  N.  basic  solution  ([OH]  =  10) 

[S"]  =  [HS'] 

The  saturation  concentration  of  hydrogen  sulphide  in 
aqueous  solution  is  very  nearly  0*1  molar.  From  Auerbach's 
measurements  we  have 

,  _  [HS'][H']  _  -8 

*  ~     [H2S]     -  y  x  x  iU 
In  this  solution 

[HS1=[H-] 
and  therefore 


[H-]  =  [HS']  =  \/0-l  X  91  x  10"8  =  0-95  x  10'4 
Further,  since 

=  — THS'l    =         * 
we  have  [S"]  =  1*2  x  10  ~15 

Again  in  1*0  M.  Na2S  solution 

[HS'][OH']  _ 
h  ~~        [S"] 
[HS']  =  [OH'] 
and  [S"]  +  [HS']  =  1'0 


130 


COMPLEX   IONS 


assuming   complete   electrolytic  dissociation.     These  equa- 
tions give 

[HS']  =  [OH']=0'91 
and  [S"]  =  0-09 

Finally,  in  a  solution  of  NaHS  we  have 


and 


,  _  [HS'][H-]       g         10»8 
kl  ~     [H2S]      ~*iX  w 

^=[H-][OH']  =  l-2  X  It)"14 


Hence  the  hydrolysis  constant,  -A,  is 

K  _  [tf2S][OH']  m  1-2  x  10-14  _  7 

hf  [HS']  9-1  x  10"*  "  X     X  iU 

In  a  1*0  M.  solution,  we  have 

[H2S]  =  [OH'] 
and  [HS']  =  1,  very  nearly 

Hence     [H2S]  m  [OH']  =  %/\*%  X  1<T7  =  3-6  X  10"4 


Now 
Hence 


[H-]  = 


10_;4=  3-3X10- 


[OH']       3-6  X  10 


[Sl^'jffl^2*10-15*1  ,3-6x10-* 
L    J         [H*]  3-3  x  10"n 


On  account  of  the  great  importance  of  these  results  we 
may  reproduce  the  following  table  (Knox),  including  the 
foregoing  and  some  others  : — 


Solution. 

[S"] 

[HS'] 

[H2S] 

[H-] 

[OH] 

l-OM.Na„S     . 

009 

0-91 

l-3xl0"7 

1-3  xlO~14 

0-91 

1-0  M.  NaHS  . 

3-6  xlO5 

1 

3-6x10-" 

3-3  x  lO"11 

3-6xl0~4 

1-0  M.  (NH4)2S 

2-4  x  HT6 

ca.  1 

5-5  x  10-3 

5xl0-10 

2-3xl0~5 

10M.NH4HS 

1-6  xl0"7 

093 

0-07 

0-7  Xl0~8 

1-7X10-6 

Sat.   aqueous  i 
H2S          / 

1-2x10   ,5 

0-95x10  4 

0-1 

0-95  x  10  -* 

1-3  xlO"10 

Sat.  H2S  +  l-(n 
N.  acetic  acid  j 

0-65  xl0~18 

2-1x10  6 

0-1 

4-2x10  3 

3xHT12 

Sat.H2S+l*0\ 
N.  HOI       J 

1-lxlO'23 

0-91  xlO8 

o-i 

1-0 

1-2x10-" 

SOME   SPECIAL  CASES   OF  EQUILIBETUM     181 

Knox  also  made  measurements  of  the  RM.F.'s  of  cells 
of  the  type 

1-0  N.  E  1 1-0  N.  KC1|01  M.  Na2S|M 

where  M  was  an  electrode  of  silver,  lead  or  copper  respec- 
tively, and  found  that  the  concentrations  of  the  metal  ions 
in  0*1  M.  Ns^S  were 

[Ag-]=6'3  x  1(T24 
[Pb»]=2-6  x  10  "12 
[Cu-]=  1-2  x  10  ~39 

A  01  M.  solution  of  NaaS  is  0*001  M.  with  respect  to  S" 
ions,  and  we  thus  obtain  the  solubility  products 

[Ag-]2[S"]  =  3-9  x  10-50 
[Pb-]  [S"]=2-6  x  10  "15 
[Cu»]  [S"]=l-2  x  10  ~42 

As  was  remarked  in  the  case  of  Bernf eld's  measurements, 
the  value  of  the  solubility  product  for  lead  sulphide  found 
in  this  way  is  incorrect.  From  the  results  for  silver  and 
copper  we  obtain  the  solubility  values  2*2  x  10  ~17  and 
11  X  10  "21  respectively. 

From  the  concentration  of  mercury  ions  in  sodium 
sulphide  solutions  saturated  with  mercuric  sulphide  we 
obtain 

[Hg--][S"]=LHgS  =  2'8xlO-« 

whence  the  solubility  of  mercuric  sulphide  in  water  is 
1/7  X  10  ~27  gram  mol.  per  litre. 

Bruner  and  Zawadski  (Zeit.  anorg.  Chem.,  65, 136  (1909) ; 
correction,  ibid.,  67,  454  (1910))  studied  several  further  cases 
of  sulphide  precipitation  analytically,  thus  avoiding  the 
errors  incidental  to  potential  measurements.  The  sulphides 
studied  in  this  way  were  those  of  thallium,  iron,  cadmium 
and  lead. 

As  the  mean  of  many  determinations  of  the  equilibrium 
point,  approached  from  both  sides,  i.e.  both  by  partial  solution 


132 


COMPLEX   IONS 


of  the  sulphide  in  acid,  and  by  precipitation  with  hydrogen 
sulphide,  the  value 

KI  =  ™§2=  0-637 
was  obtained.     Remembering  that 


this  gives  us 


L1  =  1-092  x  lO"22!^ 


Lx  =  7*0  x  KT28 


Experiments  were  also  made  on  the  precipitation  of 
thallium  sulphide  in  presence  of  other  sulphides.  The 
results  showed  that  the  equilibrium  is  affected  by  the 
sulphides  of  arsenic,  antimony,  tin,  mercury  and  copper. 
The  values  of  Kx  were  plotted  against  the  molecular  com- 
position of  the  precipitate,  and  in  this  way  it  was  shown 
that  thallium  sulphide  forms  two  compounds  with  copper 
sulphide  corresponding  to  the  forniuhe  Tl2S,4CuS  and 
Tl2S,2CuS  respectively.  From  the  fact  that  the  curve  dips 
between  these  two  points,  Bruner  and  Zawadski  consider 
that  these  two  compounds  form  a  solid  solution.  When  the 
amount  of  T12S  in  the  precipitate  exceeds  36  per  cent,  the 
constant  again  becomes  0*637,  indicating  that  the  thallium 
sulphide  is  present  as  a  separate  phase. 

With  arsenic  sulphide,  thallium  sulphide  forms  a  con- 
tinuous series  of  solid  solutions  from  pure  As2S3  to  a  solution 
containing  73*5  per  cent,  of  T12S  molecules.  When  more 
thallium  sulphide  than  this  is  present  it  appears  as  a  separate 
phase.  (For  the  recognition  of  other  solid  solutions  by  the 
study  of  equilibria  in  solution,  see  Abegg  and  Scholtz  (Zeit. 
fur  Elehtrochemie,  12  (1906)).) 

Analytical  determinations  of  the  equilibrium  point  in 
the  case  of  iron  gave 

K2  =  3-4  x  103 
L2  =  3-7  x  10  -19 

In  the  case  of  cadmium  the  results  depended  to  some 
extent  upon  the  method  of  precipitation  of  the    sulphide. 


SOME  SPECIAL  CASES   OF  EQUILIBEIUM     133 

I  Thus,  for  the  precipitation  of  cadmium  sulphide  from  the 
sulphate  solution, 

K2  =  4-6  X  10-7 

while  for  the  product  from  the  chloride, 

K2  =  6-6  X  10-6 

This  can  only  be  interpreted  by  assuming  that  cadmium 
sulphide  can  exist  in  two  or  more  modifications. 
The  analytical  results  obtained  for  lead  showed 

K2  =  3-1  X  10-6 
L2  =  8-4  x  10-28 

in  startling  contrast  with  the  values  obtained  by  Bernfeld 
(loc.  cit.)  and  Knox  (loc.  cit.)  from  potential  measurements. 
Knox's  measurements  gave  for  lead 

L2  =  2-6  x  10-15 

Thus  the  potentials  measured  by  Bernfeld  and  Knox 
appear  to  correspond  to  a  concentration  of  lead  ions  about 
1013  times  too  great,  or,  in  other  words,  the  E.M.F.  of  the 
lead  electrode  is  about  13  x  0*0295  =ca.  0*4  volt  too  high. 

Further  light  has  recently  been  thrown  on  this  point  by 
Lebedew  (Zeit.  Mektrochemie,  18,  891  (1912)).  Lebedew 
repeated  the  potential  measurements  and  obtained  constant 
and  reproducible  values  which  agreed  well  with  Bernfeld's. 
It  therefore  became  necessary  to  consider  possible  errors  in 
the  theory  for  the  cells  measured.  Experiments  were  there- 
fore made  in  order  to  ascertain  whether  the  lead-lead  sulphide 
electrode  is  really  reversible.  On  substituting  a  platinum 
plate  for  the  lead  electrode  in  a  sodium  hydrosulphide 
solution  it  was  found  that  a  definite  E.M.F.  was  produced 
which  was  almost  exactly  equal  to  that  of  a  lead  electrode 
dipping  into  the  same  liquid.  Thus  it  is  evident  that  (1) 
lead  becomes  passive  in  sodium  hydrosulphide  solution, 
(2)  that  some  other  electrochemical  reaction  occurs  at  a  lead 
or  other  indifferent  electrode  in  sodium  hydrosulphide 
solution  which  produces  a  definite  E.M.F.  The  nature  of 
this  reaction  is  unknown. 


134 


COMPLEX   IONS 


If  we  know  the  solubility  product  of  the  sulphide  of  a  metal 
whose  electrolytic  potential  we  also  know,  we  can  obtain  an 
approximate  value  for  the  electrolytic  potential  of  sulphur. 

In  a  reversible  cell  of  the  type 

Metal  |  saturated  metallic  sulphide  |  Sulphur 

if  we  pass  a  current  from  left  to  right  the  sulphide  is  formed, 
while  by  passing  the  current  from  right  to  left  we  decompose 
the  sulphide  into  its  elements.  Since  the  solution  is  in 
equilibrium  with  the  solid  sulphide,  the  free  energy  of  the 
reaction  is  the  free  energy  of  formation  or  decomposition  of 
the  solid  sulphide,  and  it  is  measured  by  wFE,  E  being  the 
decomposition  potential.  We  may  split  thisE.M.F.  into  two 
parts,  being  the  E.M.F. 's  of  the  electrodes 

Metal|Saturated  metallic  sulphide 
and  Sulphur |  Saturated  metallic  sulphide. 

In  order  that  wFE  shall  represent  the  positive  energy 
which  we  require  to  expend  on  the  system  to  decompose  one 
gram  molecule  of  the  sulphide,  we  must  reckon  the  E.M.F. 
of  the  metal  electrode  positive  when  the  electrode  is  negative 
to  the  solution,  and  the  E.M.F.  of  the  sulphur  electrode 
positive  when  the  electrode  is  positive  to  the  solution.  The 
values  taken  in  this  way  when  the  solutions  contain  one  gram 
ion  per  litre  are  the  thermodynamic  electrode  potentials,  and 
are  expressed  numerically  using  either  the  hydrogen  electrode 
or  the  normal  calomel  electrode  as  nullpoint.1 

Calling  Eg,  EA ,  and  EK  the  decomposition  potential  and 
the  electrolytic  potentials  of  the  anion  and  kation  respec- 
tively, we  obtain  the  relation 

1  Another  mode  of  expressing  these  values  is  also  in  use,  in  which  the 
signs  of  the  potentials  are  reversed.  This  has  been  used  in  the  preceding 
chapters.  In  the  system  used  in  this  section,  the  electrolytic  potential 
represents  the  relative  tendency  of  the  metal  or  non-metal  to  go  into 
solution,  while  in  the  other  system,  which  was  used  in  the  previous 
chapters,  the  electrolytic  potential  represents  the  tendency  of  the  metal 
or  non-metal  to  come  out  of  solution. 


SOME  SPECIAL   CASES   OF  EQUILIBRIUM     135 

where  ca  and  ck  are  the  concentrations  of  the  anions  and 
kations  in  gram  ions  per  litre,  and  na  and  »*  are  their 
valencies.  If  A  and  Q  be  the  free  energy  of  formation  and 
the  heat  of  formation  respectively  of  the  solid  sulphide,  we 
have 

A=Q+T§ 

If  T^r  be  small  compared  with  Q,  we  may  write 

A  =  Q 
Hence  Es  =  A  =  % 

if  Q  be  expressed  in  joules,  and  n  be  the  number  of  faradays 
required  for  the  electrolytic  decomposition  of  one  gram 
molecule  of  the  sulphide ;  or,  expressing  Q  in  calories, 


E    m     4-189Q     =  Q 

s       n  X  96540      n  X  23046 


Therefore 


Q  17        l_   ^       L    RT1         !     ■     RTT         1 

~^m  =  Ea  +  Ek  +  ^log-  +  %Flog^ 
This  gives  for  monovalent  metals 

2  x  23046         A         K     2F    DC(l  +  F     °  <■„ 
T?     if    i  P'T,     1  ,  ET .      1 

=  EA  +  EK-glog(Ca-C/) 
=  EA  +  EK-I^logL1 


Similarly,  for  divalent  metals 


=  EA  +  EK-^log(V<g 


2  x  23046         A         K      2F 

RT 
2F 


=  EA  +  KK-_tlogL2j 


136 


COMPLEX  IONS 


and  for  the  sulphides  of  the  trivalent  metals  (formula  M2S3) 


6  x  23046 


_KT 
2F 


Ea^  EK-^logCa-— logcfc 


=  EA  +  EK-glogCa3-glog^ 
=  EA  +  EK-|JlogL3 


Thus,  in  general, 


Q 


n  X  23046 


=  EA  +  EK  -  ??log  L 

A  K         wJf       o 


Now,  Bodlander  {Zeit.  phys.  Chem.}  27,  55  (1898))  showed 
that  this  general  equation,  when  solved  for  L,  gave  values  for 
the  solubilities  of  a  large  number  of  salts  which  agreed 
approximately  with  the  values  found  by  other  means.  We 
may  therefore  solve  for  EA  if  the  solubility  of  the  salt  be 
known.  This  is  the  single  method  which  has  as  yet  been  found 
for  measuring  the  electrolytic  potential  of  sulphur. 

Bruner  and  Zawadski,  in  the  course  of  their  determina- 
tion of  the  equilibrium  constant  for  thallium  sulphide, 
measured  its  temperature  coefficient.  From  this  they 
calculate 

L!(18°)  =  4-5  x  10-23 

At  18°  the  above  formula  becomes 

Q 


2  X  23046 


=  EA  +  EK-  0-029  log10  Li 


Inserting  the  values  of  Q  (19650  calories  (Thomsen)),  EK 
(0*322  volt  against  the  hydrogen  electrode  (Wilsmore,  Zeit. 
phys.  Chem.,  35,  291  (1900)))  and  L  (4*5  x  10 ~23),  we  obtain 

EA=  -0-543  volt 

against  the  hydrogen  electrode. 

Bruner  and  Zawadski  took  as  the  denominator  on  the 
left-hand  side  of  the  equation  the  value  2  x  23100,  and 
thus  found  EA  =  —0*545  volt.  The  electrolytic  potential  of 
thallium  had  been  redetermined  a  short  time  previously  by 


SOME  SPECIAL  CASES   OF  EQUILIBEIUM     137 

Brislee  (Trans.  Faraday  Soc,  Dec,  1908),  who  found  the 
value  to  be  4-  0*3195  volt  against  the  hydrogen  electrode. 

If  we  recalculate  the  electrolytic  potential  of  sulphur 
from  Bruner  and  Zawadski's  results,  using  this  value,  we 
obtain 

EA=  -0-5475  volt 

Taking  the  denominator  on  the  left-hand  side  of  the  equation 
as  23046,  however  (the  more  exact  value),  we  get 

EA=  -0-5455  volt 

Thus  the  two  small  errors  practically  neutralise  one  another, 
and  the  value  calculated  by  Bruner  and  Zawadski  is  almost 
unaffected. 

From  this  value  we  can  now  calculate  the  solubility  of 
any  other  sulphide  of  which  we  know  the  heat  of  formation. 
The  following  table  (Bruner  and  Zawadski,  loc.  cit.)  shows 
the  values  of  L  for  a  number  of  sulphides  calculated  from 
the  experimental  data  of  various  observers  relating  to  equi- 
libria in  solution  on  the  one  hand,  and  calculated  from  the 
heat  of  formation  on  the  other,  using  the  value 

EA  =  -0-545  volt 

The  values  of  Q  taken  were  those  of  Thomsen  excepting 
where  otherwise  indicated. 

Considering  the  inaccuracy  introduced  into  the  calcu- 
lations by  putting 

A  =  Q 

the  agreement  between  the  two  sets  of  values  is  excellent. 
It  may  be  noticed  that  the  error  grows  more  important  as  Q 
grows  smaller  (see,  for  example,  Nernst,  Theoretische  Chemie, 
5te  Auf.,  pp.  727,  728),  and  correspondingly  we  find  that 
the  calculated  values  (from  heat  of  formation)  lie  closest  to 
the  experimental  ones  (from  equilibrium  measurements)  in 
the  cases  where  Q  is  large.  This  comparison  affords  a 
valuable  means  of  avoiding  large  errors  in  the  experimental 
values,   such,   for  example,   as   those  yielded  by  potential 


138 


COMPLEX   IONS 


measurements  with  lead  electrodes  in  sodium  hydrosulphide 
solutions. 


Sulphide. 

Q 

EK 

L,  calculated 

from  Q. 
E4  and  ER. 

2  X  23100 

L,  observed. 

Observer. 

MnS 

0-961 

+  1-0752 

l-4xl0~15 

FeS 

0-471 

+  0-470* 

1-5X10-'9 

3-7  X10~19 

B.  &Z. 

TLS 

0-425 

+  0-322 

(4-5X10--3)1 

4-5X10"23 

0ZnS3 

0-8889 

+  0-770 

1-2X10-" 

ca.5xl0"25 

Glixelli 7 

NiS 

0-375 

4-  0-228 

1-4X10~24 

— 



CoS 

0-430 

+  0-232 

3-0X10-26 

— 



CdS 

0-700 

+  0-42011 

3-6xl0~29 

5-OxlO-29 

B.  &Z. 

PbS 

0-400 

/  +  0-151 
\+ 0-120' 

4-2xl0~28| 
3-6X10-29/ 

3-4X10"28 

>> 

CuS 

0-375 

-  0-329 

8-5X10-" 

/1-2X10"42 
\5-9xl0-42 
I3-9X10"51 

Knox7 

Immerwahr 8 

Bernfeld  " 

Ag2S 

0-072 

-  0-7986 

1-6X10"49  !{3-9xl0-50 

;|4-8xio-->3 

Knox7 
Lucas  " 

HgS 

(0-193,0\ 
\0-134   J 

/2-0xl0~52 

\i-oxio~49 

1-OxlO-53 

Knox7 

—  0*753 

6-7xl0~48 

Immerwahr ' 

1  Standard  used  in  calculating  EA. 

2  All  the  values  in  this  column  are  taken  from  Wilsmore's  table  (Zeit. 
phys.  Chem.,  35,  291  (1900)),  except  where  otherwise  stated. 

3  The  variety  precipitated  from  alkaline  solution.  The  observed  value 
of  L  is  recalculated  from  Glixelli's  results,  as  Bruner  and  Zawadski's 
value  appears  to  contain  an  error. 

4  W.  K.  Lewis's  value.  (Dissert.  Breslau,  1908 ;  Abegg's  Handbuch, 
4"  Gruppe,  p.  638). 

■  Foerster,  Beitrdge  zur  Kenntnis  des  elektrochemischen  Verhaltens  des 
Eisens,  1909. 

0  G.  N.  Lewis,  Zeit.  phys.  Chem.,  55,  473  (1906).  This  value  agrees 
with  that  found  by  Brislee  (Trans.  Farad.  Soc.,  Dec,  1908). 

7  loc.  cit. 

8  Zeit.  fur  Elektrochemie,  7,  478  (1901). 

9  Berthelot,  Thermochemie,  Paris,  1897,  II,  308. 

10  Varet  (Berthelot,  Thermochemie,  II,  359). 

n  The  electrolytic  potential  of  cadmium  was  redetermined  by  Jaques 
(Trans.  Farad.  Soc.,  Vol.  V.  Part  III  (1910)),  and  found  to  be  +0-395 
+  0-006  volt  at  25°.     This  gives  L  =  1-55  x  10 ~29. 


APPENDIX   I 


The  Hydrate  Theory 

Various  circumstances  have  led  to  a  widely  spread  belief  that 
many  electrolytes  are  "  hydrated  "  in  solution ;  that  is,  that  each 
molecule  of  solute  is  present  in  combination  with  one  or  more 
molecules  of  water.  Much  experimental  work  has  been  done,  and 
a  great  deal  of  discussion  has  taken  place  on  the  subject,  but  up 
to  the  present  very  little  definite  evidence  has  been  obtained. 

Probably  the  most  reliable  evidence  for  the  existence  of 
hydrates  in  solution  has  been  gained  by  Jones  and  his  co-workers, 
a  resume  and  bibliography  of  whose  work  was  given  by  Jones 
(Zeit.phys.  Chem.,  74,  325  (1910)). 

In  1894  Jones  (Zeit.  phys.  Chem.,  13,  416)  determined  the 
freezing  points  of  mixtures  of  sulphuric  acid  and  water  in  acetic 
acid  as  solvent.  The  results  showed  clearly  that  combination 
had  occurred,  and  was,  in  fact,  so  nearly  complete,  that  almost 
exactly  one  molecule  of  water  disappeared  for  each  molecule  of 
sulphuric  acid  added,  indicating  the  formation  of  the  hydrate 
H2S04,H20.  The  values  in  solutions  containing  more  water 
appeared  to  show  the  formation  to  a  smaller  extent  of  the 
hydrate  H2S04, 2H20.  Since  these  hydrates  are  formed  in  acetic 
acid  solution,  we  may  conclude  that  they  are  also  present  in 
aqueous  solutions  of  sulphuric  acid. 

Jones  and  Ota  (Amer.  Ghem.  Jour.,  22,  5  (1899))  in  the 
course  of  an  investigation  of  the  complex  formation  occurring 
in  solutions  of  certain  double  salts,  determined  their  freezing 
points  in  order  to  gain  an  insight  into  the  molecular  condition 
of  the  solute.  It  was  found  that  as  the  concentration  was 
increased,  the  molecular  depression  of  the  freezing  point,  instead 
of  becoming  continually  less,  passed  through  a  minimum  at  a 
concentration  between  0*1  and  0*2  molar,  and  then  increased  very 
rapidly.    The  same  phenomenon  had  already  been  observed  by 

139 


140  APPENDIX   I 

Arrhenius  (Zeit.  phys.  Chem.,  2,  496  (1888)).  This  fact  cannot 
be  explained  by  assuming  any  possible  mode  of  combination  of 
the  substances  in  solution,  since  according  to  the  law  of  mass- 
action,  dissociation  must  increase  as  the  solution  is  diluted,  and 
the  molecular  depression  must  therefore  increase  also.  Jones 
therefore  sought  to  explain  the  phenomenon  by  assuming  that  the 
solvent  entered  into  combination  with  the  solute,  forming,  in  the 
case  of  water  solutions,  "  hydrates."  If  this  occurs,  the  active 
mass  of  water  in  a  solution  will  be  less  than  that  calculated  from 
its  composition,  without  allowing  for  the  formation  of  hydrates. 
As  the  concentration  increases,  the  proportion  of  the  water 
existing  in  combination  with  the  solute  will  become  greater,  so 
that  strong  solutions  in  which  hydrates  are  present  should  behave 
with  respect  to  freezing  point  depression  as  if  they  were  a  great 
deal  stronger  than  they  really  are. 

Further  experimental  work  showed  that  a  great  many  single 
salts  show  a  minimum  in  the  molecular  depression,  and  it  was 
found  that,  in  general,  salts  which  are  hygroscopic  or  crystallise 
with  much  water  of  crystallisation  show  the  highest  molecular 
depression  in  strong  solutions. 

Later,  other  methods  were  brought  to  bear  upon  the  subject. 
It  was  shown  that  salts  which  crystallised  with  much  water 
gave  solutions  which  had  the  highest  temperature  coefficients  of 
the  electrical  conductivity.  If  we  assume,  as  seems  probable, 
that  most  hydrates  are  exothermic  compounds,  and  tend  to  dis- 
sociate with  rise  in  temperature,  it  is  evident  that  the  ionic 
volumes  will  diminish,  and  that  the  conductivity  of  a  solution 
containing  hydrated  ions  should,  ceteris  paribus,  increase  more 
rapidly  with  rise  of  temperature  than  that  of  a  solution  in  which 
the  ions  are  not  hydrated.  Further,  the  temperature  coefficient 
increased  very  fast  with  dilution  in  the  case  of  the  supposedly 
hydrated  salts,  and  much  more  slowly  in  the  case  of  the  un- 
hydrated  ones. 

Jones  has  also  observed  the  absorption  spectra  of  many 
solutions  of  metallic  salts,  and  claims  that  the  results  support 
his  theory.  He  criticises  the  theory  of  Donnan  and  Bassett 
regarding  the  colour  of  cobalt  chloride  solutions,  but  his  argu- 
ments do  not  appear  to  show  the  incorrectness  of  the  theory. 
Jones  states  that  the  dissociation  of  the  complex  ion  should 
increase  with  rise  in  temperature,  and  therefore,  if  the  colour  of 
the  solution  is  affected  by  complex  formation,  the   effect  of 


THE   HYDKATE   THEORY  141 

raising  the  temperature  should  be  opposed  to  that  of  increasing 
the  concentration,  and  spectroscopic  observations  do  not  support 
this  conclusion.  But  actually  it  was  shown  (Donnan  and  Bassett, 
loc.  cit.)  that  the  formation  of  the  complex  ion  in  cobalt  chloride 
solutions  is  probably  endothermic,  and  rise  of  temperature  should 
therefore  have  an  effect  upon  the  colour  precisely  similar  to  that 
of  increase  in  concentration,  in  good  agreement  with  the  facts. 

Walden  (Zeit.  phys.  Chem.,  55,  207  (1906))  showed  that  for  a 
given  electrolyte  (tetraethylammonium  iodide)  the  product  of 
the  viscosity  and  the  maximum  molecular  conductivity  of  a 
solution  is  independent  of  the  solvent  and  the  temperature. 
About  thirty  solvents  were  examined.  Walden  considers  that 
this  can  be  accounted  for  by  assuming  that  each  ion  carries  with 
it  some  of  the  solvent. 

Riesenfeld  and  Reinhold  (Zeit.  phys.  Chem.,  66,  672)  point 
out  that  the  ionic  mobility  should,  ceteris  paribus,  depend  upon 
the  ionic  volume,  and  should  decrease  as  the  ionic  volume 
increases.  In  the  series  of  metals  Li,  Na,  K,  Rb,  and  Cs,  the 
atomic  volume  rises  continuously  from  12  to  71,  while  the  ionic 
mobilities  also  increase  from  33*4  to  68*2.  This  can  be  explained 
by  assuming  that  the  ions  carry  with  them  various  quantities  of 
water,  the  lithium  ion  being  most  hydrated  and  the  caesium  ion 
least. 

Further,  the  temperature  coefficient  of  the  ionic  mobility  at 
infinite  dilution  is  nearly  the  same  for  many  monovalent  ions, 
and  is  equal  to  the  temperature  coefficient  of  the  fluidity  of 
water.  Thus  it  appears  as  if  the  friction  during  electrolysis 
exists  between  water  and  water.  The  same  relation  was  observed 
by  Walden  (loc.  cit.)  in  all  the  solvents  examined  by  him,  and  is 
included  in  his  law  relating  to  viscosity  and  conductivity. 

Another  method  of  attacking  the  problem  of  hydration  consists 
in  measuring  the  depression  of  the  solubility  of  a  substance  caused 
by  addition  of  an  indifferent  solute  to  the  solution.  This  subject 
is  discussed  by  Philip  (Trans.  Farad.  Soc,  Oct.,  1907),  from 
whose  paper  the  following  tables  are  taken. 


142 


APPENDIX   I 


Table  I. 
(Calculated  from  Kaopp,  Zeit.  phys.  Chem.,  48,  97  (1904)),  20°  C. 


Percentage 

Volume  of  Hydrogen  absorbed 

Hydrate. 

By 

L  litre  of  solution. 

By  1000  grams  of  water. 

4-91 

7-69 

14-56 

18-77 
29-5 

18-39 
18-02 
17-12 
16-53 
15-42 

.       18-95 
18-92 
18-78 
18-69 
19-07 

Table  II. 
(Calculated  from  Steiner,  Weid.  Ann.,  52, 275  (1894)),  15°  C. 


Percentage 

Volume  of  Hydrogen  absorbed 

Molecules  of 

water  to 

1  mol.  Cane 

Sugar. 

of  Cane 
Sugar. 

By  1  litre  of      ,   By  1000  grams 
solution.                of  water. 

o-oo 

16-67 
30-08 
47-65 

—                   18-83 
15-61                 17-55 
12-84                 16-27 

8-92                 13-95 

1 

6-5 
6-0 
5-4 

Table  III. 
(Steiner)  15° 


Volume  of  Hydrogen  absorbed 

Percentage 
of  KC1. 

Average 

molecular 

By  1  litre  of 

By  1000  grams 

Hydration. 

solution. 

of  water. 

o-oo 

18-83 

3-83 

16-67 

16-93 

10-5 

7-48 

14-89 

15-36 

9-4 

12-13 

12-79 

13-5 

8-5 

19-21 

10-12 

11-09 

7-2 

THE   HYDRATE  THEORY  143 

Table  IV. 
(Knopp)  20°. 


Percentage  of  KC1. 

Average  molecular  hydration. 

1-09 

9-8 

2-12 

11-1 

4-07 

10-0 

6-37 

10-0 

7-38 

10-0 

13-61 

7-6 

Knowing  the  density  of  the  solutions,  we  can  split  the  mass 
of  any  volume  of  the  solution  into  grams  of  water  and  solute 
respectively,  and  thus  calculate  the  volume  of  hydrogen  absorbed 
by  1000  grams  of  water,  assuming  that  the  gas  does  not  dissolve 
in  the  solute.  In  the  case  of  chloral  hydrate  the  absorption 
coefficient  calculated  in  this  way  for  the  water  alone  remains 
practically  constant,  while  for  solutions  of  cane  sugar  and  potassium 
chloride  it  decreases  quickly.  It  seems  very  probable  that  this 
decrease  is  due  to  hydration  of  the  solute,  less  free  water  being 
present  in  the  solutions  than  the  amount  calculated  from  their 
composition.  If  we  assume  that  this  is  the  case,  we  can  readily 
calculate  the  amount  of  water  that  must  have  been  removed  by 
each  molecule  of  the  solute,  and  thus  obtain  the  values  given  in 
Tables  II.,  III.,  and  IV.  Similar  measurements  have  been  made 
(Philip,  loc.  cit.),  with  many  other  salts,  and  in  each  case  the 
results  show  a  considerable  degree  of  hydration. 

The  equation  of  van  der  Waals  can  be  applied  in  many  cases 
to  strong  solutions  of  non-electrolytes  (Bredig,  Zeit.  phys. 
Chem.,  4,  44  ;  Noyes,  ibid.,  5,  83  ;  Berkeley  and  Hartley,  Trans. 
Roy.  Soc,  206,  A,  481 ;  Sackur,  Jahresbericht  der  Schlesischen 
Ges.  fiir  V aterldndische  Cultur,  86,  June,  1908)  by  assuming 
suitable  values  for  b.  The  values  of  b  obtained  in  this  way 
always  diminish  rapidly  as  the  temperature  is  raised,  however,  and 
probably  include  the  volume  of  a  quantity  of  water  in  combination 
with  the  solute,  the  hydrate  so  formed  tending  to  dissociate  as  the 
temperature  rises. 

For  a  discussion  of  the  theory  of  hydration  in  solutions,  the 
reader  is  referred  to  the  Transactions  of  the  Faraday  Society, 
Volume  III.,  Part  2  (1907)  (a  general  discussion  on  "  Hydrates  in 


144  APPENDIX   I 

Solution "  :   copies  can  be  obtained  separately),  also  Dhar,  Zeit. 
far  EleUrochemie,  20,  57  (1914). 

The  general  result  of  the  evidence  is  that  it  is  probable  that 
many  electrolytes  and  some  non-electrolytes  exist  in  solution  in 
combination  with  a  large  number  of  molecules  of  the  solvent. 
Thus,  in  many  dilute  solutions,  instead  of  free  ions  or  molecules,  ive 
are  probably  dealing  ivith  complex  compounds  of  these  with  a  number 
of  molecules  of  the  solvent.  In  dilute  solution  these  compounds 
must  be  regarded  as  of  practically  constant  composition,  and  the 
quantity  of  solvent  thus  combined  is  negligible  compared  with 
the  amount  present  in  the  system.  In  strong  solutions,  on  the 
other  hand,  as  the  concentration  is  altered,  considerable  alterations 
may  occur  in  the  composition  of  the  hydrates,  and  further,  the 
active  mass  of  the  solvent  may  be  much  less  than  that  calculated 
from  the  composition  of  the  solution  with  respect  to  solvent  and 
solute.  This  theory  affords  a  probable  explanation  of  the  deviations 
from  the  law  of  mass  action  shown  by  many  strong  solutions,  and 
appears  likely  to  become  useful  in  explaining  some  of  the  difficulties 
met  with  in  applying  the  law  of  mass  action  to  strong  solutions, 
but  it  does  not  affect  the  results  obtained  in  dilute  solutions 
where  the  methods  discussed  in  this  volume  point  to  the  existence 
of  comparatively  stable  complex  ions. 


APPENDIX   II 

A  Theoretical  Method  of  examining  Certain  Solutions 

The  following  method  provides  for  the  complete  analysis  of 
any  solution  containing  complex  ions  of  the  type  MAW,  where  M 
represents  an  atom  of  a  metal  and  A  an  acid  radicle. 

We  assume  that  a  series  of  potential  measurements  in  solutions 
containing  a  fixed  amount  of  alkali  salt  of  the  acid  and  various 
quantities  of  the  salt  of  the  metal  M  has  shown  that  q,  the 
number  of  atoms  of  metal  in  the  complex  ions,  has  the  usual 
value,  1.  g  is  really  the  average  value  for  all  the  compounds 
present  in  the  solution.  It  cannot  be  less  than  1  for  any  com- 
pound, and  thus  if  we  find  the  average  value  to  be  1  it  follows 
that  q  must  be  1  for  all  the  compounds  (undissociated  salt  and 
complex  ions  and  salts)  in  the  solution. 

We  now  proceed  to  make  a  series  of  potential  measurements  in 
solutions  containing  a  fixed  amount  of  the  salt  of  the  metal,  M, 
and  variable  amounts  of  alkali  salt.  In  these  solutions,  the  total 
concentration  of  the  metal,  c,  is  made  up  of  the  concentration  of 
free  metal  ions,  together  with  those  of  a  series  of  compounds  of 
the  metal  with  the  acid  radicle,  A,  including  undissociated  salt 
and  complex  ions.     We  therefore  obtain 

c  =  [M-]  +  [MA]  +  [MA2']  +  [MAa"]  +  .  .  .  +[MAJ 
Calling  the  dissociation  constants  of  the  compounds  MA,  MA2', 
MA3",  .  .  .  MAU,   Kl9   K2,   K3  .  .  .  Kn,  and  using   n   different 
concentrations  of  alkaline  salt,  we  have 

-CM^i+^+^+^-+...+m.:) 

145  L 


146  APPENDIX   II 

This  set  of  equations  can  be  solved  for  Ku  K2,  K3,  .  .  .  K„, 
and  we  thus  find  the  formulae,  dissociation  constants  and  concen- 
trations of  all  the  compounds  in  the  solution. 

Practically,  the  method  has  the  disadvantage  that  small  errors 
in  the  potential  measurements  become  greatly  magnified  in  the 
calculation.  Also,  the  concentration  of  alkali  salt  must  be  large 
compared  with  the  total  concentration  of  the  metal,  to  enable  us 
to  calculate  the  concentration  of  the  ion  A',  while  on  the  other 
hand  the  concentrations  of  the  different  solutions  used  must 
differ  widely  from  one  another.  The  method  has  never  been 
applied  successfully  to  a  'set  of  experimental  results,  but  it  is 
nevertheless  useful  in  enabling  us  to  form  a  conception  of  the 
state  of  affairs  in  a  solution  containing  more  than  one  complex  ion. 

We  have  worked  out  the  expressions  for  a  monovalent  metal, 
but  obviously  those  for  a  di-  or  trivalent  one  would  be  precisely 
the  same,  the  first  two  or  three  constants  corresponding  to  the 
undissociated  salt  and  its  different  stages  of  dissociation. 


NAME   INDEX 


A 


Abbott,  32,  33 

Abegg,  2-5,  25,  26,  45,  85,  86,  92, 

106,  110-118,  126,  132 
Abel,  36,  105-110 
Archibald,  52,  53 
Arrhenius,  92,  140 
Auerbach,  120,  122 


Daneel,  126 
Dawson,  27,  59,  74 
Denharn,  100 
Dhar,  144 
Dolezalek,  82 
Donnan,  97-100,  140 
Drucker,  72 


Basset,  97-100,  140 

Beckmann,  21 

Behrend,  105 

Bein,  98 

Benratb,  99,  100 

Berkeley,  143 

Bernfeld,  120,  138 

Berthelot,  20,  138 

Biltz,  99 

Bjerrum,  43,  44 

Bodlander,  2-5,  34,  46,  73-84, 

87,  109,  121,  126,  136 
Bonsdorff,  93 
Bottger,  116 
Bredig,  59,  143 
Breest,  59,  61 
Brislee,  137 
Bruner,  131-133,  136-138 


Gentnerszwer,  96 
Cox,  86 
Crozier,  85 
Cumming,  42,  45 


E 
«   Eberlein,  34,  87,  121 


Fittig,  73-84,  86 
Foerster,  138 
Fox,  93-96 


G 

86,       Gaus,  74,  77,  88-93 
Gawler,  27 
Glixelli,  121,  138 
Goodson,  27 
Goodwin,  82 


H 

Haber,  126 
Hamburger,  26,  85 
Hantzsch,  91 
Hartley,  143 
Heimbucher,  108 
Henderson,  42 
Hittorf,  12-17 


147 


148 


NAME   INDEX 


Immerwahr,  138 


Jakowkin,  1,  25,  26 
Jaques,  30,  47,  65,  69-72,  138 
Joannis,  85 
Johnson,  G.  S.,  26 
Johnson,  K.  R.,  42,  43 
Jones,  100,  139,  140 
Jungfleisch,  20 


Kahlenberg,  101 
Kendall,  34 
Knopp,  142,  143 
Knox,  120-131,  138 
Kohlrausch,  82,  116 
Kohlschutter,  99 
Konowalaw,  74 
Ktister,  102,  126,  128 


Labendzinski,  46 
Lebedew,  133 
Leblanc,  12,  49-52,  126 
Lewis,  G.  N.,  99,  138 
Lewis,  W.  K.,  63-69,  138 
Ley,  108 
Loeb,  70 
Lucas,  87, 121,  138 

M 

Maitland,  25,  110-118 
Masson,  18, 101-103 
McBain,  17 
McCrae,  27,  74 
Miahle,  49 
Miolati,  9 

N 

Nernst,  20,  21,  30,  70,  137 
Noyes,  12,  18,  30-33,  49-52, 143 


Ogg,  105 
Ota,  139 


Penfield,  26,  112,  118 
Philip,  141-143 
Pick,  61-63, 107 
Pickering,  89 
Planck,  42,  43 


Reinhold,  19, 141 
Reychler,  74,  85 
Richards,  36,  52,  53,  105 
Riesenfeld,  19,  92,  141 
Roloff,  1,  21-24 
Rothmund,  89,  93 


S 


Sabatier,  98 

Sackur,  143 

Sand,  59,  61 

Scholtz,  132 

Sebaldt,  91 

Setschenoff,  26 

Sherill,  36,  37,  53-61,  108 

Shukoff,  106 

Spencer,  115 

Steele,  18, 101-108 

Steiner,  142 

Storbeck,  109 


Thiel,  83 
Thomsen,  136 
Tower,  43 
Trotsch,  98 


NAME  INDEX 


149 


Varet,  138 
Vogel,  63 
Volhard,  63 


W 


Waals,  van  der,  143 
Walden,  96, 141 
Walton,  59 


Wells,  26, 112, 118 
Werner,  9, 10 
Wheeler,  26 
Whetham,  18 
Wildermann,  26 
Wilsmore,  186, 138 
Worley,  24 


Zawadski,  131-133, 136-138 


SUBJECT  INDEX 


Absorption  spectra,  140,  141 
Ammonia,  active  mass  of,  77 

,  pressure  of,  88-93 

,  solubility  of  silver  salts  in,  76, 

80-83 
Ammonium  hydrosulphide,  130 

sulphide,  130 

Atoms,  free,  2 


Barium  bromide,  72 
—  chloride,  18,  72 
Bodlander's  theorem,  46-48 
Bromine,  21-26 
Bismuth  sulphide,  121 


C 


Cadmium  acetate,  69-72 

chloride,  13 

hydroxide,  92 

iodide,  13 

sulphide,  133,  138 

Calomel,  solubility  of,  108 
Catalysis,  52,  59,  60,  128 
Cobaltammine  salts,  8-10 
Cobalt  chloride,  97-100 

sulphide,  138 

Complex  compounds, 
definition  of,  3 
Copper  chloride,  99 

hydroxide,  93 

Cryoscopic  measurements,  49 
Cuprammonium  ion,  27,  93^ 
Cupric  sulphide,  131,  138 


Cuprous  and  cupric  sulphides,  110 
Cuprous  chloride,  109 


D 


Diffusion  potential,  41 
-,  elimination  of,  43-45 


E 


Electroaffinity,  2,  3 
Electrode  potential,  40 
Electrolytic  potential,  40 
Energy  of  formation,  free,  134,  135 


Eehling's  solution,  101-103 
Ferrous  sulphide,  132,  138 
Freezing  point  of  solutions,  21, 139, 
140 


H 


Heat  of  formation,  135 
Hydrogen  sulphide,  120,  128, 130 
Hydrosulphide  ion,  130 


Ionic  velocity,  variation  in,  18 


Lead  acetate,  69-72 

nitrate,  63-69 

sulphide,  121,  131,  133,  138 


150 


SUBJECT   INDEX 


151 


M 


Manganese  sulphide,  138 
Mercuric  cyanide,  54-59 
— ~  halides,  49-61,  72 

sulphide,  black,  122 

,  red,  122-127,  138 

Mercurous  ions,  concentration  of, 

in  calomel  electrode,  108 
Migration  of  ions,  10,  18 
Molecular  compounds, 

definition  of,  4 

N 

Nickel-ammonia  salts,  93 
Nickel  hydroxide,  93 
sulphide,  138 


Oxy-acids,  4 


Periodic  Table,  2 
Platinammine  salts,  8,  9 
Polyhalides,  26,  27 
Potassium  cadmium  iodide,  15-17 

ferrocyanide,  3,  14,  15 

nitrate,  63-69 


Silver-ammonia  chloride,  73 

complex,  74-88,  93^ 

, cyanide,  87-88 

Silver  bromide,  80-83 
chloride,  74-84 


Silver  cyanide,  7,  11,  12,  87 

nitrite,  61-63 

oxide,  93 

—  sulphide,  121,  131,  138 

thiocyanate,  86,  87 

Sodium  hydrosulphide,  120, 126, 130 

sulphide,  122-125,  130 

,  hydrolysis  of,  123,  127, 

128 
Solubility,  depression  of,  29-34 

,  divergence  from 

calculated  value  of,  34 

product,  28 

Solute,  indifferent,  141-143 
Sulphur  dioxide,  93-96 

ion,  126-138 

,  electrolytic  potential  of,  136, 

137 


Thallic  iodide,  complex,  112-118 
Thallium  iodides,  110 
Thallous  sulphide,  131,  132,  138 
Trihalides,  26 


Valency,  2-4 


W 


Water  of  crystallisation 
and  conductivity,  140 


;   Zinc  chloride,  72 
hydroxide,  93 

I    sulphide,  121,  138 


THE  END 


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